PHYSICS QUESTIONBANK 2017 XIIth CBSE BOARD EXAM

A NAME IN CONCEPTS OF PHYSICS

XI &XII (CBSE & ICSE BOARD)

IIT-JEE / NEET /AIIMS / JIPMER / uptU y

ELCTROSTATIC FORCE & FIELD 1.

(UNIT - 1)

An electrostatic field line cannot be discontinuous why?

O 0.1 m

[CBSE 2005]

2.

Define electric field intensity. Write its S.I unit. Write the magnitude and direction of electric field intensity due to an electric dipole of length 2a at the mid-point of the line joining the two charges. [CBSE 2005]

3.

Three point charge of +2  C, – 3  C and –3  C are kept at the vertices, A, B and C respectively of an equilateral triangle of side 20 cm as shown in the figure. What should be the sign and magnitude of the charge to be placed at the mid-point (M) of side BC so that the charge at A remains in equilibrium? [CBSE-2005]

0.1 m z

Ex = ax, where a = 500 N/C-m , E y = 0, EZ = 0 Calculate (i) the flux through the cube, and (ii) the charge inside the cube. 8.

9.

+2 C A

B

–3 C

4.

5.

M 20cm

–3 C

A positive point charge (+q) is kept in the vicinity of an uncharged conducting plate. Sketch electric field lines originating from the point on to the surface of the plate. Derive the expression for the electric field at the surface of charged conductor . [CBSE BOARD 2009] [CBSE BOARD 2009]

The electric field E due to a point charge at any point F near it is defined as E lim , where q is the test q 0 q charge and F is the force acting on it. What is the physical significance of lim q  0 in this expression? Draw the electric field lines of a point change Q when (i) Q > 0 and (ii) Q < 0. [CBSE 2007] Define electric flux. Write its S.I S.I units. A spherical rubber balloon carries a charge that is uniformly distributed over its surface. surface. As the balloon is blown up and increases in size, how does the total electric flux coming out of the surface change ? Give reason.

(a) The

mutual forces between two charges do not get affected by the presence of other charges. (b) The potential, due to a dipole, at any point on its axial line, is zero. 11.

12.

(a) A charge +Q is placed on a large spherical conducting shell of radius R. Another small conducting sphere of radius r carrying charge „q‟ is introduced

inside the large shell and is placed at its centre. Find the potential difference between two points, one lying on the sphere and the other on the shell. (b) How would the charge between the two flow if they are connected by a conducting wire? Name the device which works on this fact [CBSE BOARD 2009]

Calculate the work done to dissociate the system of three charges placed on the vertices of a triangle as shown. Here q = 1.6 × 10 –10 C [CBSE 2007]

The electric field components due to charge inside the cube of side 0.1 m as shown: [CBSE BOARD 2008]

Two charges +Q and –Q are kept at ( –x2, 0) and (x 1, 0) respectively in the x – y plane. Find the magnitude and direction of the net electric field at the origin (0, 0) [CBSE 2009]

13.

7.

Two point charges 20 x 10–6 C and –4 x 10–6 C are separated by a distance of 50 cm in air. (i) Find the point on the line joining the charges, where the electric potential is zero . [CBSE BOARD 2008] (ii) Also find the electrostatic potential energy of the system.

or the following statements: 10. Point out „right‟ or „wrong‟ f or

C

[CBSE 2007]

6.

x

A spherical conducting shell of inner radius r 1 and outer radius r 2 has a charge „Q‟. A point charge „q‟ is placed at the centre of the shell. [CBSE BOARD 2010] (a) What is the surface charge density on the (i) inner surface (ii) outer surface of the shell ? (b) Write the expression for the electric field at a point x > r2 from the centre of the shell ?

QUESTION BANK FOR CLASS XII (CBSE BOARD-2017) BOARD-2017)

P.L . SHARMA ROAD, ROAD, center SHASTRI NAGAR NAGAR center CENTRAL MARKET, Opp. Sagar Complex Meerut

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XI &XII (CBSE & ICSE BOARD) 14.

IIT-JEE / NEET /AIIMS / JIPMER / uptU

Show that the electric field at the surface of a charged  conductor is given by E  nˆ , where  is the  0 surface charge density and n is a unit vector normal to the surface in the outward direction ˆ

[CBSE BOARD 2010]

15.

16.

Two small identical electrical dipole AB and CD, each of dipole moment 'p' are kept at an angle of 120º as shown in the figure. What is the resultant dipole moment of this combination? If this system is subjected to electric field will be the ( E ) directed along + X direction, what will magnitude and direction of the torque acting on this?

22.

[CBSE 2011]

A dipole is present in an electrostatic elec trostatic field of magnitude 106 N/C. If the work done in rotating it, from its position of stable equilibrium to its position of unstable equilibrium, equals 2 × 10 –23 J, find the magnitude of the dipole moment of this dipole. [CBSE BOARD 2010] Figure shows three point charges +2q, – q and + 3q. Two charges + 2q and – q are enclosed within a surface „S‟. What is the electri c flux due to this configuration through the surface „S‟ [CBSE 2010]

B

23.

Two point charges having equal charges separated by 1m distance experience a force of 8 N. What will be the force experienced by them, if they are held in water, at the same distance? (Given: K water = 80) [CBSE 2011]

17.

In which orientation, a dipole placed in a uniform electric field is in (i) stable, (ii) unstable equilibrium? [CBSE 2010]

State Gauss's law. Use it to deduce the expression for the electric field due to a uniformly charged thin spherical shell at points (i) inside and (ii) outside the shell. [CBSE 2011]

25.

Define electric dipole moment. Write its S.I. S.I. unit .[CBSE 2011]

18. (a) Depict

the equipotential surfaces for a system of two identical positive point charges placed a distance

„d‟ apart.

24.

26.

[CBSE BOARD 2010]

(b) Deduce

the expression for the potential energy of a system of two point charges q 1 and q 2 brought from

(i) Draw the equipotential surfaces of the system (ii) Why do the equipotential surfaces get closer to each other near the point charges?

infinity to the points r 1 and r 2 respectively in the presence of external electric field . 19. A

proton is placed in a uniform electric field directed along the positive x-axis. In which direction will it tend to move? [CBSE BOARD 2011]

20.

(a) Draw Draw equipotential surfaces due to a point charge Q > 0. (b) Are these surfaces equidistant from each other? If not explain why. [CBSE BOARD 2011]

21.

A point charge Q is placed at point O as shown in the figure. Is the potential difference V A – VB positive, negative or zero, if Q is (i) positive (ii) negative?

Two point charges 3  C and –3  C are placed at points A and B apart. . [CBSE 2011]

27. A hollow metal

sphere of radius 10 cm is charged such that the potential on its surface is 5V. What is the potential at the centre of the sphere? [CBSE 2011]

28.

A thin straight infinitely long conducting wire having charge density  is  is enclosed by a cylindrical surface of radius r and length l, its axis coinciding with the length of the wire. Find the expression for the electric flux through the surface of the cylinder. [CBSE 2011]

29.

Why must electrostatic field be normal to the surface at every point of a charged conductor? [CBSC 2012]

[CBSE 2011]

30.

Draw a plot showing the variation of (i) electric field (E) and (ii) electric potential (V) with distance r due to a point charge Q.






32.


Explain the principle of device that can build up high voltages of the order of a few million volts. Draw a schematic diagram and explain the working of this device. [CBSE 2012] Is there any restriction on the upper limit of the high voltages set up in this machine? Explain. (a) Define electric flux. Write its S.I.units.

point due to a uniformly charged infinite plane sheet is independent of the distance from it. (c) How is the field directed if (i) the sheet is positively charged, (ii) negatively charged ?

35.

Very Short Answer Type Questions: [01 Mark Each] 1.

Name the dielectric whose molecules have (i) non-zero and (ii) Zero dipole moment.

2.

Define dielectric constant of a medium. medium. What is the value value of dielectric constant for a metal?

3.

What happens happens to the energy energy stored in a capacitor if, if, the plates of a charged capacitor are moved farther, the battery remaining connected?

4.

Distinguish between polar and non-polar dielectrics.

5.

An air capacitor capacitor isis given given a charge of 2mC raising its potential potential to 200 V . If on inserting a dielectric medium its potential falls to 50 V, what is the dielectric constant of the medium?

6.

In what form is the energy stored in a charged charged capacitor?

7.

On what factors factors does the capacitance of a parallel plate capacitor with dielectric depend?

8.

On inserting a dielectric dielectric between the plates plates of a capacitor, capacitor, its its capacitance is found to increase 5 times, what is the relative permittivity of the dielectric?

9.

How does does the the electric electric field inside a dielectric dielectric decrease when it is placed in an external electric field?

[CBSE 2012]

(b) Using Gauss‟s law, prove that the elec tric field at

34.

ELECTRIC POTENTIAL, ENERGY & CAPACITORS

A test charge 'q' is moved without acceleration from A to C along the path from A to B and then B to C in electric field E as shown in the figure (i) Calculate the potential difference between A and C. (ii) At which point (of the two) is the electric potential more and why? [CBSE 2012]

An electric dipole is held in a uniform electric field. (i) Show that the net force acting on it is zero. (ii) The dipole is aligned parallel to the field. Find the work done in rotating it through the angle of 180°.

CBSE PROBLEMS

(LAST 10 YEARS)

1.

Obtain the expression for the capacitance of a parallel plate capacitor. Three capacitors of capacitances C 1, C2 and C 3 are connected (i) in series, (ii) in parallel. show that the energy stored in the series combination is the same as that in the parallel combination. [CBSE 2003]

2.

the graph shows the variation of voltage, „V‟ across the

[CBSE 2012]

plates of two capacitors A and B versuls increase of charge, „Q‟ stored on them. Which of the two

capacitors has higher capacitance? Give reason for your answer. [CBSE 2004]

3.

Find the total total energy stored in the capacitors in the given network. [CBSE 2004]







On charging a parallel plate capacitor to a potential V, the spacing between the plates is halved, and a dielectric medium of εr = 10 is introduced between the plates, without disconnecting the d.c. source. Explain, using suitable expressions, how the [CBSE 2008] (i) capacitance, (ii) electric field and (iii) energy density of the capacitor change.

A 10 F capacitor is charged by a 30 V d.c. supply and then connected across an uncharged 50 F capacitor. Calculate (i)The final potential difference across the combination, (ii) the initial and final energies. How will you account for the difference in energy? [CBSE 2004]

5.

(a) Why does the electric field inside a dielectric decreases when it is placed in an external electric field? (b) A parallel plate capacitor with air between the plates has a capacitance of 8pF. What will be the capacitance if the distance between the plates be reduced by half and the space between them is filled with a substance of dielectric constant K = 6?

12.

Three identical capacitor C 1,C2 and C3 of capacitance 6mF each are connected to a 12 V battery as shown Find [CBSE 2009]

[CBSE-2005 - 06, 2 Marks]

6.

A 12pF capacitor is connected to a 50 V battery. How much electrostatic energy is stored in the capacitor.

(i) charge on each capacitor (ii) equivalent capacitance of the network (iii) energy stored in the network of capacitors

[CBSE-2005]

7.

A parallel plate capacitor is to be designed with a voltage rating 1kV using a material of dielectric constant 3 and dielectric strength about 10 7 Vm–1. For safety we would like the field never to exceed say, 10% of the dipole strength. What minimum area of the plates is required to have a capacitance 50 pF

13.

A parallel plate capacitor capaci tor is charged by a battery. After some time the battery is disconnected and a dielectric slab of dielectric constant K is inserted between the plates. How would (i) the capacitance, (ii) the electric field between the plates and (iii) the energy stored in the capacitor, be affected ? Justify your answer. [CBSE 2009]

14.

A network of four capacitors each of 12 F capacitance is connected to a 500 V supply as shown in figure. Determine (a) Equivalent capacitance of the network and (b) Charge on each capacitor [ CBSE 2010]

15.

A parallel-plate capacitor is charged to a potential difference V by a dc source. The capacitor is then disconnected from the source. If the distance between the plates is doubled, state with reason how the following change: [CBSE 2010]

[CBSE-2005]

8.

9.

Two capacitors of capacitance of 6 F and 12 F are connected in series with a battery. The voltage across the 6F capacitor is 2V. Compute the total battery voltage. [CBSE 2006] A parallel plate capacitor, each with plate area A and separation d, is charged to a potential difference V. The battery used to charge it is then disconnected. A dielectric slab of thickness d and dielectric constant K is now placed between the plates. When change, if any, will take place in [CBSE 2007] (i) Charge on the plates (ii) Electric field intensity between the plates (iii) Capacitance of the capacitor Justify your answer in each case.

10.

Explain the underlying principle of working of parallel plate capacitor. If two similar plates, each of area A having surface charge densities +  and – are separated by a distance d in air, write expressions for. (i) the electric field at points between the two plates. (ii) the potential difference between the plates. (iii) the capacitance of the capacitor so formed. [CBSE 2007]

11.

Derive an expression for the energy stored in a parallel plate capacitor.

(i) Electric field between the plates (ii) Capacitance, and (iii) Energy stored in the capacitor







Figure shows two identical capacitors, C 1 and C 2, each of 1 mF capacitance connected to a battery of 6V. Initially switch 'S' is closed. After sometime 'S' is let open and dielectric slabs of dielectric constant K = 3 are inserted to fill completely the space between the plates of the two capacitors. How will the (i) charge and (ii) potential difference between the plates of the capacitors be affected after the slabs are inserted? [CBSE 2011]

Give the colour coding for a carbon resistor of 1 ohm having 5% tolerance? 13. If the temperature of a metallic conductor increases how does the relaxation time of electrons in conductor change? dimensional formula formula of mobility of electrons. 14 Write the dimensional 15. Manganin is used in making standard resistance .give two reasons. 16. How does the drift velocity of electrons in a metallic conductor change, if the length of the conductor is doubled by stretching it, keeping the applied potential difference constant? 12.

1.

17.

Net capacitance of three identical capacitors in series is 1 F. What will be their net capacitance if connected in parallel? Find the ratio of energy stored in the two configurations if they are both connected to the same source. [CBSC 2011]

18.

Deduce the expression for the electrostatic energy stored in a capacitor of capacitance 'C' and having charge'Q' [CBSC 2012] How will the (i) energy stored and (ii) the electric field inside the capacitor be affected when it is completely c ompletely filled fil led with a dielectric material of dielectric constant 'K' ?

CURRENT ELECTRICTY One mark questions

Define drift velocity of an electron How does the drift drift velocity of electrons in a metallic conductor vary with increase in temperature? A steady current flows in a metallic conductor of non-uniform 3. cross-section. Explain which of these quantities is constant along the conductor: Current, current density, electric field and drift speed? The potential potential difference difference across a given copper wire wire is 4. increased. What happens to the drift velocity of the charge carriers? Explain, how does the resistivity of a conductor depend upon 5. (i) number density (n) of free electrons and (ii) Relaxation time (t) 6. What do you mean by e.m.f. of a cell? It is easier to start a car engine engine on a warm day than on a 7. chilly day. Why? 8. The wire of a potentiometer potentiometer should be of uniform uniform area area of cross-section. Why? Name the device used for measuring the internal resistance of 9. a secondary cell. 10. Under what conditions will Terminal potential difference of a cell be greater than its EMF? 11. A wire of resistivity  is stretched to twice its length. What will be its new resistivity? 1. 2.

What is meant by the sensitivity of a potentiometer? A battery E1 of 4V and variable resistance R h are connected in series with the wire AB of the potentiometer. The length of the wire of the potentiometer is 1 metre. When a cell E 2 of e.m.f. 1.5 volt is connected between points A and C, no current flows through E 2. Length of AC = 60 cm . [CBSE 2003]

(i) Find the potential difference between the ends A and B of the potentiometer. (ii) Would the method work, if the battery E 1 is replaced by a cell of e.m.f. of 1V? 2. Are the paths of electrons straight lines between successive collisions (with positive ions of the metal) in the (i) absence of electric field (ii) presence of electric field? [CBSE 2003] (iii) Establish a relation between drift velocity „vd‟ of an electron in a conductor of cross- section „A‟, carrying current „i‟ and concentration „n‟ of free electrons per

unit volume of conductor. Hence obtain the relation between current density and drift velocity. 3. The circuit diagram shows the use of a potentiometer to measure a small emf produced by a thermocouple connected between X and Y. The cell C, of emf 2V, has negligible internal resistance. The potentiometer wire PQ is 1.00 m long and has resistance 5 Ω. The balance point s is found to be 400 mm from P. Calculate the value of emf V, generated by the thermocouple. [CBSE 2004] Cell emf = 2.00V

P Q

995 Thermocouple

X Hot junction

Y Cold junction






Deduce the condition for balance in a Wheatstone Wheatstone Bridge. Using the principle of Wheatstone Bridge, describe the method to determine the specific resistance of a wire in the laboratory. Draw the circuit diagram and write the formula used. write any two important precautions you would observe while performing the experiment . [CBSE 2003-04]

5.

Define the term „resistivity and wri te its S.I. unit, Derive


the expression for the resistivity of a conductor in terms of number density of free electrons and relaxation time [CBSE 2005]

6.

7.

8.

You are given 'n' n' resistors, each of resistance 'r'. These are first connected to get minimum possible resistance. In the second case, these are again connected differently to get maximum possible resistance. Compute the ratio between the minimum and maximum values of resistance so obtained . [CBSE 2006] Draw a circuit diagram using a meter bridge and write the necessary mathematical relation used to determine the value of an unknown resistance. Why cannot such an arrangement be used for measuring very low resistance? [CBSE 2006]

If the galvanometer deflection at the end B is (i) More, (ii) less, than that the at the end A, which of the two faults, listed above, would be there in the circuit?

Give reasons in support of your answer in each case. 11. A number of identical cells, n, each of emf E, internal resistance r connected in series are charged by a d.c source of emf E‟. using a resistor R. [CBSE 2008] (i) Draw the circuit arrangement. (ii) Deduce the expressions for (a) the charging current and (b) the potential difference across the combination of the cells. 12.

Sate Kirchhoff‟s rules of current distribution in an

electrical network. Using these rules determine the value of the current I 1 in the electric circuit given below. [CBSE 2007]

9.

(i) Calculate unknown emf of the cell. (ii) Explain with reason, whether the circuit works, if the driver cell is replaced with a cell of emf 1 V. (iii) Does the high resistance R, used in the secondary circuit affect the balance point ? Justify your answer.

The given figure shows a network of resistances R1, R2, R3 and R4. [CBSE 2007]

13.

Using Kirchhoff‟s laws, establish the balance condition

for the network.

A potentiometer wire of length 1m is connected to a driver cell of emf 3 V as shown in the figure . When a cell of 1.5 V emf is used in the secondary circuit, the balance point is found to be 60 cm. On replacing this cell and using a cell of unknown emf, the balance point shifts to 80 cm. [CBSE 2008]

The figure shows experimental set up of a meter bridge. When the two unknown resistance x and y are inserted the null point D is obtained 40 cm from the end A. when a resistance of 30 Ω is connected in series with x, the null point shift by 10 cm. find the position of the null point when 30 Ω resistance is instead of X connected in series with Y determine the value of X and Y [CBSE 2009] X

10.

For the potentiometer circuit shown in the given figure, points X and Y represent the two terminals of a unknown emf E‟. A student obs erved that when the jockey is moved from the end A to the end B of the potentiometer wire, the deflection in the galvanometer remains in the same direction. [CBSE 2007] What may be the two possible faults in the circuit that could result in this observation ?

Y

G A

D

C ()







A wire of 15 W resistance is gradually stretched to double its original length. It is then cut into two equal parts. These parts are then connected in parallel across a 3.0 volt battery. Find the current drawn from the battery. [CBSE 2009] 15. Two conducting wires X and Y of same diameter but different materials are joined in series across a battery. If the number density of electron in X is twice that in Y, find the ratio of drift velocity of electrons in the two wires. [CBSE 2010] 16. In a meter bridge, the null point is found at a distance of l 1 cm from A. If now a resistance of X is connected in parallel with S, the null point occurs at l 2 cm. Obtain a formula for X in terms of l 1, l2 and S. [CBSE 2009, 10] 14.

X R

S G

A

B

Write the principle of working of a potentiometer. Describe briefly, with the help of a circuit diagram, how a potentiometer is used to determine the internal resistance of a given cell. [CBSE 2010,2011] 18. In the meter bridge experiment, balance point was observed at J with AJ = l. [CBSE 2010] (i) The values of R and X were doubled and then interchanged. What would be the new position of balance point? (ii) If the galvanometer and battery are interchanged at the balance positions how will the balance point get affected. 17.

19.

In the circuit shown, R 1 = 4 Ω, R 2 = R 3 = 15 Ω, R 4 = 30 Ω and E = 10 V. Calculate the equivalent resistance of the circuit and the current in each resistor. [CBSE 2011]

20.

(c) Outline the necessary steps to convert a galvanometer of resistance R G into an ammeter of a given range. [CBSC 2011] 21. A cell of emf E and internal resistance r is connected to two external resistances R 1 and R2 and a perfect ammeter. The current in the circuit is measured in four different situations: (i) Without any external resistance in the circuit (ii) With resistance R 1 only (iii) With R1 and R 2 in series combination (iv) With R1 and R 2 in parallel combination The currents measured in the four cases are 0.42 A, 1.05 A, 1.4A and 4.2 A, A, but not necessarily in that order, Identify the currents corresponding to the four cases mentioned above. [CBSE 2012] 22. In the figure a long uniform potentiometer wire AB is having a constant potential gradient along its length. The null points for the two primary cells of emf ε1 and ε 2 connected in the manner shown are obtained at a distance of 120 cm and 300cm. from the end A Find (i) ε1 /ε2 and (ii) position of null point for the cell ε1. How is the sensitivity of a potentiometer increased? [CBSE 2012]

23. Using Kirchhoff‟s rules determine the value of unknown

resistance R in the circuit so that no current flows through 4 W resistance. Also find the potential difference between A and D.

24.

Calculate the value of the resistance R in the circuit show in the figure so that the current in the circuit is 0.2 A. What would be the potential difference between points B and E? [CBSE 2012]

(a) State the principle of the working of a moving coil galvanometer, giving its labelled diagram. (b) "Increasing the current sensitivity of a galvanometer may not necessarily increase its voltage sensitivity." Justify this statement.







MAGNETIC EFFECT OF CURRENT Very Short Answer Type Questions:

13. What

is the angle of dip at a place where horizontal

and vertical components of earth‟s field are equal?

[01 Mark Each]

Short Answer Type Questions: [02 Marks Each]

Magnetic field lines can be entirely confined within the core of a toroid, but not within a straight solenoid. Why? 2. A beam of a particles projected along + x- axis, experiences a force due to a magnetic field along the +y axis. What is the direction of the magnetic field? 1.

3.

Write the expression for Lorentz magnetic force on a particle of charge 'q' moving with velocity v in a magnetic field B . Show that no work is done by this force on the charged particle. [CBSC 2011] 2011]

4.

Two particles A and B of masses m and 2m have charges q and 2q respectively. Both these particles moving with velocities v 1 and v 2 respectively in the same direction enter the same magnetic field B acting normally to their direction of motion. If the two forces F A and F B acting on then are in the ratio of 1 : 2, find the ratio of their velocities. [CBSE BOARD 2011]

What are the ways of producing magnetic field? Give two differences between magnetic lines of force and electric lines of force. 7. A charge q moves in a magnetic field B with a velocity v making an angle of 30° with B .What will be the magnitude of the force acting on the charge? 8. The speed of a charged particle moving in a magnetic field does not change. Why? (2003) 9. Write the expression for the force acting on a length d of a conductor carrying a current i and placed in a magnetic field B . 10. Write the definition of magnetic field B . 11. A proton is moving in a uniform magnetic field. What will be the path of the proton, if its initial direction is (i) parallel to the field (ii) Perpendicular to the field (iii) At an angle with the field. 12. Write the formula for the magnetic force acting between two parallel moving charges, explaining the meanings of the symbols used. (UPB 2005)

is projected with a velocity of 10 5 ms –1 at right angles to a magnetic field of 0.019 G. Calculate the radius of the circular path described by the electron, if e = 1.6 × 10 –19 C, m = 9.1×10 –31 kg. 15. A small compass needle of magnetic moment 'M' and moment of inertial 'I' is free to oscillate in a magnetic field 'B'. It is slightly disturbed from its equilibrium position and then released. Show that it executes simple harmonic motion. Hence write the expression for its time period. [CBSE BOARD 2011] 16. In an atom, an electron is revolving with uniform speed of 5.0 × 10 6 ms–1 in a circular orbit of radius 0.5 × 10–10 m around its nucleus. Calculate the magnetic field produced at the centre of the orbit, Given: m0 / 4p = 10–7 weber/ampere-meter and e = 1.6 × 10–19 coulomb. (2002) 17. A thin solenoid solen oid of length len gth 20 cm has single layer of 500 turns of fine wire and carries a current of 4.0 × 10–3 A. Calculate the intensity of the magnetic field on the axis at the mid-point and at the ends of the solenoid. 27. A circular segment of radius R metre subtends an angle of a radian at its centre. A current of i ampere is flowing in it in the direction shown. Find the magnitude and direction of magnetic field at the centre. (2005) 14. An electron

5. 6.

CBSE PROBLEMS 1.

(LAST 10 YEARS)

Where on the earth‟s surface is the value of vertical component of the earth‟s magnetic field z ero? The horizontal component of the earth‟s magnetic field at a given place is 0.4 × 10 –4 Wb/m2 and angle of dip

is 30°. Calculate the value of (i) Vertical component, (ii) The total intensity of the earth‟s magnetic field. 2.

In the diagram below is shown a circular loop carrying current I. show the direction of the magnetic field with the help of lines of force. [CBSE 2004]

3.

Explain with the help of diagram the terms (i) magnetic declination and (ii) angle of dip at a given place.






State and explain Biot- Savart‟s law for the magnetic field due to a current element. [CBSE 2004]

5.

Two long parallel straight wires wires X and Y separated by a distance of 5 cm in air carry currents of 10A and 5A respectively in opposite directions. Calculate the magnitude and direction of the force on a 20 cm length of the wire Y. [CBSE 2004]

6.


Using Biot-Savart‟s law, deduce an expression for the magnetic field on the axis of a circular current loop. Draw the magnetic field lines due to circular current carrying loop. [CBSE 2004]

Figure shows a rectangular current carrying loop placed 2 cm away from a long, straight, currentcarrying conductor. What is the direction and magnitude of the net force acting on the loop? (CBSE 2005, 2009, 2011)

11.

An electrons is moving along +ve x-axis in the presence of uniform magnetic field along +ve y-axis. What is the direction of the force acting on it [2007]

12.

Distinguish the magnetic properties of Dia, - Para and Ferro-magnetic substances in terms of (i) Susceptibility, (ii) Magnetic permeability and (iii) Coercivity. Give one example of each of these materials. Draw the field lines due to an external magnetic field near a (i) diamagnetic, (ii) Paramagnetic substance [CBSE 2003, 2004, 2005, 2007, 2010].

13.

What is the direction of the force acting on a charged particle q, moving with a velocity v in a uniform magnetic field B ? [CBSE-2008]

14.

Define magnetic susceptibility of a material. Name two elements one having positive susceptibility and the other having negative susceptibility .What does negative susceptibility signify? [CBSE-2008]

15.

Magnetic field lines can be entirely confined within the core of a toroid, but not within a straight solenoid. Why? [CBSE 2009]

16.

An electron does not suffer any deflection while passing through a region of uniform magnetics filed. What is the direction of the magnetic field? [CBSE 2009]

17.

Write the expression for the magnetic moment ( m ) due to a planar square loop of side „ l‟ carrying a steady current I in a vector form [CBSE 2010] In the given figure this loop is placed in a horizontal plane near a long straight conductor carrying a steady current I1 at a distance l as shown. Give reason to explain that the loop will experience a net force but no torque. Write the expression for this force acting on the loop.

charge „q‟ travels with 7. A hydrogen ion of mass „m‟ and charge a speed „v‟ in a circle of radius „r‟ in a magnetic field of intensity „B‟. Write the equation in terms of these

quantities only, relating the force on the ion to the required centripetal force. Hence derive an expression for its time period. [CBSE 2004] 8.

State and p rove Ampere‟s circuital law .

9.

Explain the principle and work in of a cyclotron with

[CBSE 2004]

the help of labelled diagram. A cyclotron‟s oscillator

frequency is 10 MHz what should be the operating magnetic field for accelerating protons? If the radius radius of its „Dees‟ is 60cm, what is the kinetic energy of the

proton beam produced by the accelerator? Express your answer in units of Me V. (e = 1.60 × 10 –19 C, m = 1.67 × 10 –27 kg, 1MeV= 1.62 × 10–13 J.) [CBSE 2004, 2005, 2006, 2007, 2009, 2011]

10.

Depict the magnetic field lines due due to two straight, long parallel conductors carrying currents I 1 and I2 in the same direction, Hence deduce an expression for the force acting per unit length on one conductor due to the other. Is this force attractive or repulsive?







A long straight wire of a circular cross-section cross -section of radius „a‟ carries a steady current „ I‟. The current is uniformly distributed across the cross- section. Apply Ampere‟s

ELECTROMAGNETIC INDUCTION Very Short Answer Type Questions:

[01 Mark Each]

circuital law to calculate the magnetic field at a point „r‟

in the region for (i) r < a and (ii) r > a . 19.

[CBSE 2010]

A beam of a particles projected along + x- axis, experiences a force due to a magnetic field along the +y axis. What is the direction of the magnetic field? [CBSE 2010]

1.

Magnetic flux f in weber in a closed circuit of resistance 10W varies with time t (sec) as Φ = 6t 2 – 5t + 1. Find magnitude of induced current at t = 0.25s?

2.

Does the change in magnetic flux induce emf or current? Show that Lenz's law is a consequence of the law of conservation of energy. State a rule to determine the direction of current induced due to the motion of a conductor in a perpendicular magnetic field. In the figure, the movable wire is moved to the left, causing an induced current as shown. What is the direction of B in the region A?

3. 4.

5.

A 20.

Deduce the expression for the magnetic dipole moment of an electron orbiting around the central nucleus. [CBSE 2010]

21.

As shown in figure, a conducting rod AB moves parallel to X-axis in a uniform magnetic field, pointing in the positive Z-direction. The end A of the rod gets positively charged. Is this statement true? Give reason.

6.

The permeability of magnetic material is 0.9983. Name the type of magnetic material it represents. [CBSE 2011]

22. A

magnetic needle free to rotate in a vertical plane parallel to the magnetic meridian has its north tip down at 60º with the horizontal. The horizontal component of the earth's magnetic field at the place is known to be 0.4 G. Determine the magnitude of the earth's magnetic field at the place. [CBSE 2011]

23. a)

Using Ampere's circuital law, obtain the expression for the magnetic field due to a long solenoid at a point inside the solenoid on its axis. [CBSE 2011] (b) In what respect is a toroid different from a solenoid? Draw and compare the pattern of the magnetic field lines in the two cases. (c) How is the magnetic field inside a given solenoid made strong?

7.

A time-dependent magnetic field is associated with an electric field. Is this true or false? Justify.

CBSE PROBLEMS

(LAST 10 YEARS)

1.

Two circular coils, one of radius r and the other of radius R are placed coaxially with their centres coinciding. For R >>r, obtain an expression for the mutual inductance of the arrangement . [CBSE 2004]

2.

What are eddy currents? Discuss briefly any one application of eddy current. [CBSE 2004]

3.

A circular coil of N turns turns and radius R, is kept normal to a magnetic field, given by B = B 0 cos t. Deduce and expression for e.m.f. induced in this coil. State the rule which helps to detect the direction of induced current. [CBSE 2004]







A bar magnet M is dropped so that it falls vertically through the coil C. The graph obtained for voltage produced across the coil vs. time is shown in figure (b). [CBSE 2004] magnet

(b) Deduce an expression for the mutual inductance of two long coaxial solenoids but having different radii and different number of turns. [CBSE 2009] 11. A plot of magnetic flux (  ) versus current (I) is shown in the figure for two inductors A and B. Which of the two has larger value of self-inductance? [CBSE 2010] 12.

v

Coil C

R

(a)

(i) Explain the shape of the graph. (ii) Why is the negative peak longer than the positive peak? 5.

What is induced emf? Write Faraday‟s law of electromagnetic induction. Express it mathematically.

13. State Faraday‟s law of electromagnetic induction.

Figure shows a rectangular conductor PQRS in which the conductor PQ is free to move in a uniform magnetic field B perpendicular to the plane of the paper. The field extends from x = 0 to x = b and is zero for x > b. Assume that only the arm PQ possess resistance r. When the arm PQ is pulled outward from x = 0 with constant speed v, obtain the expressions for the flux and the induced emf. Sketch the variations of these quantities with distance 0  x  2b . [CBSE 2010]

A conducting rod of length „ l‟, with one end pivoted, is rotated with a uniform angular speed „ ‟ in a vertical plane, normal to a uniform magnetic field „B‟. Deduce

an expression for the emf induced in this rod 6.

Describe briefly, with the help of a labelled diagram, the basic elements of an A.C. generator. State its underlying principle. Show diagrammatically how an alternating emf is generated by a loop of wire rotating in a magnetic field. Write the expression for the instantaneous value of the emf induced in the rotating loop. [CBSE 2008, 2010, 2011]

[2004]

In the figure given below, a bar magnet moving towards the right or left induces an emf in the coil (1) and (2). Find given reason, the directions of the induced currents through the resistors AB and CD when the th e magnet is moving (a) towards the right, and (b) towards the left. [CBSE-2005, 2 Marks]

x=0 x=b 7.

Define self-inductance and its S.I. unit. Derive an expression for self- inductance of a long, air-cored solenoid of length, l, radius r, and having N number of turns. [CBSE 2005]

8.

Define magnetic flux. Give its SI unit. I

9.

A 0.5 long metal rod PQ completes the circuit as shown in the figure.

10.

14. A

current is induced in coil C 1 due to the motion of current carrying coil C 2. [CBSE 2011] (a) Write any two ways by which a large deflection can be obtained in the galvanometer G. (b) Suggest an alternative device to demonstrate the induced current in place of a galvanometer.

[CBSE 2006]

The area of the circuit is perpendicular to the magnetic field of flux density 0.15 T. If the resistance of the total circuit is 3 W, calculate the force needed to move the rod in the direction as indicated with a constant speed of 2 ms –1 [CBSE BOARD 2006]

x = 2b

15.

A bar magnet is moved in the direction indicated by the arrow between two coil PQ and CD. Predict the directions of induced current in each coil. [CBSE 2012]

(a) State Le nz‟s law. Give one example to illustrate this law. “The Lenz‟s law is a consequence of the principle of conservation of en ergy.” Justify this statement.







the bulb change if an iron rod is inserted in the coil? Give reasons in support of your answer.

ALTERNATING CURRENT Very Short Answer Type Questions: 1.

[01 Mark Each]

An electric Lamp is connected in series with a long solenoid of copper wire and with air core. When the combination is connected to an a.c. source, the bulb glows producing the desired illumination. Now if an iron rod is inserted inside the solenoid, explain what will happen and why?

Ans:

decreases

A galvanometer connected in an A.C. circuit does does not show any deflection. Why? ANS: A galvanometer measures mean value of a.c., which is zero over a cycle. 10.

2.

State the phase relationship between the current flowing and the voltage applied in an a.c. circuit for (i) a pure resistor and (ii) a pure inductor.

3.

A 44 mH inductor is connecting to 220 V, 50 Hz ac supply. Determine the r.m.s value of current in an a.c. circuit.

capacitor blocks D.C. but allows A.C to pass through it. Explain. Why?             ANS: -   

4.

If the the frequency of the a.c. source source in a series LCRcircuit is increased, how does the current in the circuit change?

12. Can

why?

(a) Define power factor, State the conditions under which it is (i) maximum and (ii) minimum. (b) What is the power dissipated by an ideal inductor in ac circuit?

13. Calculate

5.

6.

A power transmission line feeds input input power at 2300 V to a step-down transformer with its primary windings having 4000 turns. What should be the number of turns in the secondary in order to get output power at 230 V?

7. Why

does metallic piece become very hot when it is surrounded by coil carrying high frequency alternating current? Ans: high frequency ac produces changing magnetic flux and the large eddy currents produce heat.

11. A

we use transformer to step up D.C. voltage? If not,

Magnetic flux linked with Primary coil does not vary with time so no Induced emf in secondary.

ANS:

the r.m.s value of alternating current shown in the figure.

2A. 14. The algebraic sum of potential drop across the various – elements in LCR circuit is not equal to the applied voltage. Why? ANS: Voltages across different elements of the LCR circuit are not in same phase. ANS:

15. Fig 8.

In the circuit shown below, R represents an electric bulb. If the frequency of the supply is doubled, how should the values of C and L be changed so that glow in the bulb remains unchanged?

Ans: 9.

shows a light bulb (B) and iron cored inductor connected to a DC battery through a switch (S). (i) What will one observe when switch (S) is closed? (ii) How will the glow of the bulb change when the battery is replaced by an ac source of rms voltage equal to the voltage of DC battery? Justify your answer in each case.

I should decrease and c should increase

An air cored coil L and a bulb B are connected in series to the mains as shows in the given figure: The bulb glows with some brightness. How would the glow of

(i) brightness of the bulb increases slowly (ii) brightness remains same

Ans: -







Short Answer Type Questions: [02 Marks Each] 1. 2. 3.

4.

Write some advantage and disadvantages of a.c. over d.c Find the time required for a 50 Hz alternating current to change its value from zero to the r.m.s. value. A coil has an inductance 0.7 henry and is joined in series with a resistance of 220 W. Find the wattles component of the current in the circuit, when an alternating e.m.f. of 220 volt at a frequency of 50 Hz is supplied to it. An air core coil and an electric bulb are connected in series across a 220 V, 50 Hz a.c. source. The bulb glows with some brightness. How will the glow of the bulb be affected on introducing a capacitor in series in circuit? Justify your answer.

5.

(a) Obtain the expression for the magnetic energy stored in a solenoid in terms of magnetic field B, area A and length of the solenoid. (b) How does this magnetic energy compare with the electrostatic energy stored in a capacitor?

6.

What are the various various energy losses in a transformer? How can they be reduced? students X, Y, and Z performed an experiment for studying the variation of alternating current with angular frequency in a series LCR circuit and obtained the graphs as shown. They all used a.c sources of the same r.m.s. value and inductances of the same value. What can we (qualitatively) conclude about the (i) capacitance value (ii) resistance values Used by them? In which case will the quality factor be maximum? What can we conclude about nature of the impedance of the set up at frequency o?

9. Figure

shows an inductor L and a resistance R connected in parallel to a battery through a switch. The resistance R which of the bulbs lights up earlier, when K is closed? Will the bulbs be equally bright after same time?

ANS: - (i) The bulb B2 will light up earlier.

(ii) The bulb B1 will grow more brightly. 10. Figure

shows two electric circuits A and B. Calculate the ratio of power factor of the circuit B to the Power factor of the circuit A.

7. Three

(i) decreases from x to z (ii) decreases from x to z in case of x quality factor is more, impedance decreases from x to z

Ans:

8. When a circuit element „X‟ is connected across an a.c.

source, a current of √2A flows through it and this

current is in phase with the applied voltage. When another element „Y‟ is connected across the same a.c. source, the same current flows in the circuit but it leads the voltage by π/2 radians.(i) Name the circuit elements X and Y. (ii) Find the current that flows in the circuit when the series combination of X and Y is connected across the same a.c. voltage. Ans: - (i) x is resistor (ii) y is capacitor

√  . inductor L of reactance XL is connected in series with a bulb B to an A.C. source as shown in the figure. Briefly explain, how does the brightness of the bulb change when (a) Number of turns of the inductor is reduced and (b) A capacitor of reactance XC =XL is included in series in the same circuit.

ANS: 11. An

ANS: -

12.

(a) Bulb will grow more brightly. (b) Brightness of the bulb will become maximum.

Figure (a), (b) and (c) Show three alternating circuits with equal currents. If frequency of alternating emf be increased, what will be the effect on currents In the three cases. Explain.

(i) No effect (ii) current will decrease (iii) Current will Increase.

ANS: -






CBSE PROBLEMS 1.

2.

3.

4.


(LAST 10 YEARS)

What is choke coil? Why is it preferred to resistance in a.c. (CBSE 2003) circuit? In figures (a), (b) and (c) are shown three a.c. circuits with equal currents. If the frequency of e.m.f. be increased, then what will be the effect on the currents flowing in them? Explain with reason.

Distinguish between reactance and impedance. impedance. When a series combination of a coil of inductance L and a resistor of resistance R is connected across A 12V, 50Hz supply, a current of 0.5 A flows through the circuit. the current differs in phase from applied voltage by π /3 radian. Calculate the (CBSE 2003/06) value of L and R. A town situated situated 20km away from from a power plant generating power at 440 V, requires 600 kW of electric power at 200 V. The resistance of the two wire line carrying power is 0.4 Ω per km. The town gets power from the line through a 3000 – 220V step down transformer at a substation in the town (i) Find the line power losses in the form of heat (ii) How much power must the plant supply, assuming there [CBSE 2003] is negligible power loss due to leakage? In a series R–C circuit, R = 30 Ω, C = 0.25 mF, V = 100V and  = 10,000 radian per second. Find the current in the circuit and calculate the voltage across the resistor and the [CBSE 2004] capacitor Is the algebraic sum of these voltages more than the source voltage? If yes, resolve the the paradox.

5.

Derive the expression of power in LCR circuit.

6.

A bulb and capacitor are connected in series to an a.c. source of variable frequency. frequency. How will the brightness brightness of the bulb change on increasing the frequency of the a.c source ? Give [CBSE 2005] reason.

[CBSE 2004, 2006]

7.

8.

9.

12.

Given below are two electric circuits A and B Calculate the ratio of power factor of the circuit B to the power factor of [CBSE 2007] circuit A.

13.

In a series LCR circuit, The voltages across an inductor, a capacitor and a resistor are 30 V, 30 V and 60 V respectively. What is the phase difference between the applied voltage and [CBSE 2007] the current in the circuit?

14.

Calculate the current drawn by the primary of a transformer which steps down 200V to 20 V to operate a device of resistance 20 W. Assume the efficiency of the transformer to [CBSE 2007] the 80%

15. Explain the term „inductive reactance‟. Show graphically the

variation of inductive reactance with frequency of the applied [CBSE 2003, 2007, 2011] alternating voltage. 16. Explain the term „capacitive reactance‟. Show graphically the

17. 18.

19.

20.

What do you you mean by power factor? On what factors does itit [CBSE BOARD 2006] depend?

variation of capacitive reactance with frequency of the applied alternating voltage. An a.c. voltage E = E0 sin wt is applied across a pure capacitor of capacitance C. Show mathematically that the current flowing through it leads the applied voltage by a [CBSE 2003, 2007, 2008] phase angle of π /2. Derive an expression for the impedance of an a.c. circuit [CBSE 2008] consisting of an inductor and a resistor. An inductor 200 mH, capacitor 500 mF, resistor 10 W are connected in series with a 100 V. variable frequency a.c source. Calculate the (i) Frequency at which the power factor of the circuit is unity (ii) Current amplitude amplitude at this frequency frequency (iii) Q- factor The instantaneous current and voltage of an a.c. circuit are given by i = 10 sin 300 t V. What is the power dissipation in [CBSE 2008] the circuit? A coil Q is connected to low voltage bulb B and placed near another coil P as shown in the figure. Give reasons to explain [CBSE 2010] the following observations: (a) The bulb „B‟ lights (b) Bulb gets dimmer if the coil Q is moved towards left. B

An alternating voltage of frequency f isis applied applied across across a series LCR circuit. Let f r be the resonance frequency for the circuit. Will the current in the circuit lag, lead or remain in phase with [CBSE BOARD 2006] the applied voltage when (i) f > f r, (ii)f < f r ? Explain your answer in each case. What do you mean by the impedance of LCR - circuit Q

[CBSE 2007]

10. Distinguish between the terms „average value „and „r.m.s.

value‟ of an alternating current. The instantaneous current

from an a.c source is I = 5 sin (314t) ampere. What are the [CBSE 2007] average and r.m.s. values of the current? 11. Explain with the help of a labelled diagram the underlying principal and working of a step -up transformer. why cannot such a device be used to step-up d.c. voltage ?

AC Source Source

21.

P

A series LCR circuit is connected to a source having voltage v = vm sin  t. Derive the expression for the instantaneous current I and its phase relationship to the applied voltage. Obtain the condition for resonance to occur. Define „power factor‟. State the conditions under which it is

(i) maximum and (ii) Minimum.

[CBSE 2007, 2009, 2011]







ELECTROMAGNETIC WAVES Short Answer Type Questions: [01 Marks Each] 1.

Does the colour of radiation depend on its frequency or on wavelength? Ans: Frequency

2.

What physical quantity is the same for X-rays of A 0 wavelength 1 , green light of wavelength 5500A & radiation of wavelength 21cm? Ans: Speed.

3.

Electromagnetic radiations with wavelength: 1. λ 1 is used to kill germs in water purifiers.

2. λ 2 is used in T.V communication system. Solution: 1) λ corresponds to ultraviolet spectrum. 1 2) λ 2 corresponds to radio waves. 4. Name EM waves are used in telecommunication. Ans: Micro-wave 5.

Mention the law, that which asserts that the electric field lines cannot form close loops? Ans: Gauss’s law

6.

If the area of the TV telecast is to be doubled then what will be the height of the transmitting antenna? Double

7.

The energy of the electromagnetic wave is in the order of 15KV. To which part of the spectrum does it belong? Ans: X-rays because λ = = 0.825A  What happens happens to the average temperature on the surface of the earth if there is no atmosphere?

8.

Ans: Increases

Which of the physical quantity is NOT transported by the EM waves? Ans: Charge 10. What is condition for obtaining displacement current between the plates of the capacitor? Ans: By varying potential difference. 11. Why is the quantity ε0 dΦE /dt called the displacement current? Solution: Due to change in electric field. 12. Using a d.c source, a capacitor has has been fully charged. What are the magnitudes of conduction and displacement currents? 13. What is the ratio of speed of infrared and ultraviolet rays in vacuum? Solution: Same as velocity of light. 14. An electromagnetic wave consists of oscillating electric and magnetic fields. What is the phase relationship between these oscillations? Solution: 90o

Short Answer Type Questions: Questions: [02 Marks Each] 15.

Radio waves diffract predominately around building while light waves, which are also electromagnetic waves, do not. Why? 16. What are the characteristics properties of electromagnetic waves? 17. Mention the pair of space and time varying E and B fields which would generate a plane EM wave travelling in the z-direction Ex and By 18. Why stationary charges & constant currents do not produce electromagnetic waves? Solution: A stationary charge & constant current produce a constant electric field & constant magnetic field respectively. A constant electric field can't generate a magnetic field likewise a constant magnetic field cannot generate a electric field. Hence, EM waves can't be produced. If the electric field field that constitutes an electromagnetic wave conservative? Justify your answer. Solution: No, the electric field produced by a time varying magnetic field is non-conservative. So that electric field that constitutes the EM waves is non-conservative. 20. The radio waves, the infrared, the visible ray are EM radiations. Then how are they different from each other? Solution: They are different because the way they interact with matter is different. Interaction depends on the energy of the EM waves, which in turn depends upon its frequency (E=hv). 19.

Short Answer Type Questions: [03 Marks Each]

9.

Electromagnetic waves with wavelength (i) 1 is used to treat muscular strain. (ii) 2 are used by a FM radio station for broadcasting (iii) 3 are used to detect fracture in bones (iv)4 is absorbed by the ozone layer of the atmosphere. Identify and name the part of electromagnetic spectrum to which these radiations belong. Arrange these wavelengths in decreasing order of magnitude. (ii) radio waves, Solution: (i)  rays, (iii) X-rays, (iv) UV rays 22. (a) Which of the following, if any, can act as a source of electromagnetic waves? (i) A charge moving with a constant velocity. (ii) A charge moving in a circular orbit. (iii) A charge at rest. 21.







(b) Identify the part of the electromagnetic spectrum to which waves of frequency (i) 1020 Hz (ii) 10 9 Hz belong to microwaves. Solution: i) X-rays ii) microwave.

Give

reason:

23. Suppose

that the electric field of an electromagnetic radiation wave in vacuum is 6

E = 3.1N/C cos {(1.8rad/m) y+ (5.4 × 10 rad/s) t} 1) What is wavelength, λ ? 2) What is frequency, ν? 3) What is magnitude of the magnetic field of the wave? Solution: 1) λ =2 =2 π /k= 3.5m. 6 2) ν= /2π = 5.4x10 /2π = 0.86MHz. 8 3): B = E /c = 3.1/3x10 = 10nT. 0

(a)

Long distance radio broadcasts use short-wave bands. Why? (b) It is necessary to use satellite for long distance TV transmission. Why? (c) Optical and radio telescopes are built on the ground but X-ray astronomy is possible only from satellites orbiting the earth. Why? (d) If the earth did not have an atmosphere, would its average surface temperature be higher or lower than what it is now?

0

24. Although

in an electromagnetic wave the ratio of the electric field to the magnetic field is a constant still we say that the vision of our eye is due to only electric field. Solution: The vision of our eye is due to the force experienced by the moving charge on our retina. The moving charge experiences force both due to electric & magnetic fields. F = q E, E F = q VB B

F /F = E/V = C/V. E

B

8.

C/V>10 Therefore moving particle oscillates primarily due to the electric field. 25. A

plane electromagnetic wave travels, in vacuum, along the y-direction. Write (i) The ratio of the magnitude, (ii) The directions of its electric and magnetic field vectors. (iii) For an electromagnetic wave traveling along ydirection, its electric and magnetic field vectors are along z-axis and x-axis respectively. The direction of ⃗  ⃗ is same as that of direction of wave propagation and     ̂ 

26.

Suppose that the electric field amplitude of an electromagnetic wave is E 0=120 NC-1 and that its frequency is v=50.0 MHz (a) Determine, B 0, , k and . (b) Find expressions for E and B.

27.

Answer the following questions: questions:







Short Answer Type Questions:

RAY OPTICS Very Short Answer Type Questions:

[01 Mark Each]

1.

Out of speed, frequency and wavelength, name the parameters which remain same after reflection

2.

Suppose that one one half of the reflecting surface of a concave mirror is covered with black soot. How will the image of an object placed in front of the mirror be affected?

3.

Can we obtain the image of a real real object formed by a convex convex mirror on the screen? Does the apparent depth of a tank of water change if viewed obliquely? If so, does the apparent depth increase or decrease? Define refractive index of a medium.

4.

5.

24.

List some advantages of a reflecting telescope, especially for high resolution astronomy.

25. An

object is placed in front of convex mirror of radius of curvature 20 cm. Its image is formed 8 cm behind the mirror. Find the distance of the object from the mirror.

26. A

ta n k is fi ll e d wi t h wa t er t o a h e i g ht o f 1 2 . 5 cm The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be 9.4 cm. What is the refractive index of water? If water is replaced by a liquid of refractive index 1.63 up to the same height, by what distance would the microscope have to be moved to focus on the needle again?

What are the factors on which the normal shift depends? How can a convex convex lens behave like a diverging lens? Although the surface of a goggle goggle lens are curved, curved, it does not not have any power. Explain, why

27 . The

9.

Why do lenses of large aperture aperture suffer from spherical spherical aberration?

28 . Explain

10.

Does dispersive power of the material of a prism depend depend on the shape, size and angle of the prism? Explain?

29 .

6. 7. 8.

Why is rainbow formed in the sky? violet light 12. An object is seen first in red light and then in violet through a simple microscope. In which case is the magnifying larger? ann objective in compound 13. Why is the focal length of a microscope little shorter than the focal length of the eyepiece? 14. You are provided with four lenses of focal length 1 cm, 3cm, 10cm and 100cm. Which two would you prefer for a microscope and which two for a telescope? convex lens, when it is 15. What happens to focal length of a convex immersed in water? support the wave nature of 16. Which of the following does not support light? 17. What type of a lens is an air bubble inside water? Give Give reason also. 18. A lens whose radii of curvature curvature are different different is forming the image of an object placed on its axis. If the lens is placed with its faces reversed, will the position of the image change? incident on one face of an 19. A ray of light is normally incident equilateral prism. Trace the course of the ray through the prism and emerging from it. 20. What will be the colour of the sky in the absence of atmosphere? 22. Why do clouds appear white? increase the range of a telescope by increasing increasing the 23. Can we increase diameter of its objective?

[02 Marks Each]

sun is seen a little before it rises and for a short while after it sets. Explain, why?

11 .

the formation of mirage.

Explaining the critical angle ang le of incidence, establish relationship between the critical angle of incidence and refractive index of the denser medium, considering the rarer medium to be air of refractive index unity. How can a right angled prism be used to invert the path of a beam of light?

Long Answer Type Questions: 30. 31. 32. 33. 34 .

[04 Mark Each]

Establish mirror formula for a concave mirror. State the sign conventions used. Define magnification. Derive expressions for the magnification produced by a concave mirror. Discuss the phenomenon phenomenon of refraction through a prism. Prove the formula:  = A ( – 1) Draw a labelled ray diagram of a reflecting (Cass grain) telescope and explain its working. Figure shows a convex spherical surface with centre of curvature C, separating the two media of refractive indices n 1 and n 2 , Draw a ray diagram showing the formation of the image of a point object O lying on the principal axis. Derive the relationship between the object and image distance in terms of refractive indices of the media and the radius of curvature R of the surface.







Draw a ray diagram to show the formation of image of an object placed between the pole and centre of curvature of a concave mirror, Derive the formula connecting object distance (u), image distance (v) and focal length (f) for this particular case for the given concave mirror. State clearly the assumptions and sign conventions used. a ray diagram to show the formation of image of an object placed between the optical centre and focus of a thin convex lens. Write two characteristics of the image formed. Using this diagram, derive the relation between object distance u, image distance v and focal length f of the convex lens. Draw the graph showing the variation of v with u.

4.

A right-angle crown glass prism with critical c ritical angle 41° is placed before an object, PQ, in two position position as shown in the figure (i) and (ii). Trace the paths of the rays from P and Q passing through the prism in the two cases. [CBSE 2005]

5.

A ray of light falls on a mirror normally. What are the values of angle of incidence and the angle of reflection?

36 . Draw

37. Draw

a graph to show the variation of the angle of deviation d with that of the angle of incidence i for a monochromatic ray of light passing through a glass prism of refracting angle A. Hence, deduce the reaction, sin( A   m ) / 2  =

[CBSE 2005] 6.

What is far-sightedness or hypermetropia? What causes hypermetropia How this defect is corrected? [CBSE 06]

7.

A double convex lens of glass of refractive index 1.6 has its both surfaces of equal radii of curvature of 30 cm each. An object of height 5 cm is placed at a distance of 12.5 cm from the lens. Calculate the size of the image formed. [CBSE 2007]

8.

A convex mirror always produces a virtual image of real object independent of the location of the object. use mirror equation to prove it. [CBSE 2007]

9.

A converging lens of refractive index 1.5 is kept in a liquid medium having the same refractive index. What would be the focal length of the lens in the medium?

sin A / 2

CBSE PROBLEMS 1.

(LAST 10 YEARS)

An object is placed in front of a right angled prism ABC in two positions (a) and (b) as shown. The prism is made of crown glass with critical angle of 41°. Trace the path of two rays from P and Q., (i) in (a), normal to the hypotenuse and (ii) in (b), parallel to the hypotenuse. [CBSE 2003]

[CBSE 2008]

(a) 2.

3.

10 . A

(b)

Draw a ray diagram to show the formation of the image of an object placed between f and 2f of a thin concave lens. Deduce the relation between the object distance, the image distance and the focal length of the lens under this condition. [CBSE 2003] Draw the the graph to show the variation of angle of deviation d with the variation of angle of incidence „i;‟ for a monochromatic ray of light passing through a prism of refracting angle A. Deduce the relation between minimum deviation dm, incident angle i and refractive index of prism m . [CBSE 2003]  A   m  sin 

 

 sin

2

 

A

ray of light passing through an equilateral triangular glass prism from air undergoes minimum deviation when angle of incidence incidenc e is 3/4th of the angle of prism. Calculate the speed of light in the prism. [CBSE 2008,02]

11 .

An equi-convex equi-conve x lens, with radii of curvature of magnitude 10 cm each, is put over a liquid layer poured on top of a plane mirror. A small needle, with its tip on the principal axis of the lens, is moved along the axis until its inverted real image coincides with the needle itself. The distance of the needle, from the lens, is measured to be 15 cm. On removing the liquid layer and repeating the experiment the distance is measured to be 10 cm. Given that the two values of the distance measured represent the force length values in the two cases, calculate the refractive index of the liquid. [CBSE 2008,3]

2





XI &XII (CBSE & ICSE BOARD) 12 .

13.

14.


(a) For a ray of light travelling from a denser medium of refractive index n 1 to a rarer medium of refractive n2 index n2, prove that = sin ic, where ic is the n1 critical angle of incidence for the media. (b) Explain with the help of a diagram, how the above principle is used for transmission of video signals using optical fibres. [CBSE 2008, 5] (a) Derive the lens formula

1



1

far point of a myopic person is 80cm in front of the eye. What is the power of the lens required to enable him to see very distance objects clearly? In what way does the corrective lens help the above person? Does the lens magnify very distance object? Explain .

1

, for a concave f v u lens, using the necessary ray diagram. (b) Two lenses of powers 10 D and –5D are placed in contact. [CBSE 2008, 5] (i) Calculate the power of the new lens. (ii) Where should an object be held from the lens, so as to obtain a virtual image of magnification 2? –

20. The

[CBSE 2009, 3]

21.

(a) (i) Draw a labelled ray diagram to show the formation of image in an astronomical telescope for a distant object. (ii) Write three distinct advantages of a reflecting type telescope over a refracting type telescope. (b) A convex lens of focal length 10 cm is placed coaxially 5 cm away from a concave lens of focal length 10 cm. If an object is placed 30 cm in front of the convex lens, find the position of the final image formed by the combined system. [CBSE 2009]

22.

(a) Draw the ray diagram showing the geometry of formation of the image of a point object situated on the principal axis, and on the convex side, of a spherical surface of radius of curvature R. Taking the rays as incident from a medium of refractive index n 1 to another of refractive index n 2, show that

A ray of light passing through an equilateral triangular glass prism from air undergoes minimum deviation when angle of incidence is 3/4 th of the angle of prism. Calculate the speed of light in the prism . [CBSE 2003]

15. (a) Draw

a ray diagram showing the passage of light through a glass prism. Hence obtain a relation between the angles of deviation, incidence and emergence and the angle of prism. (b) Show that no ray can pass through a prism whose refracting angle A is greater than twice the critical angle for the material of the prism. [CBSE 2008, 5]

n2

–

v 16.

A glass lens of refractive index 1.5 is placed in a trough of liquid .What must be the refractive index of the liquid in order to mark the lens disappear ? [CBSE 2008]

17.

(a) Draw the ray diagram for the formation of image of an object by a convex mirror and use it (along with the sign convention) to derive the 'mirror formula.

are convex mirrors used as side view mirrors in

n2 – n1

R

23.

(a) With the help of a suitable ray diagram, derive the mirror formula for a concave mirror. (b) The near point of a hypermetropic person is 50 cm from the eye. What is the power of the lens required to enable the person to read clearly a book held at 25 cm from the eye? [CBSE 2009]

24.

State the conditions for the phenomenon of total internal reflection? (H.S.S.C.E. 2010; C.B.S.E. 2010)

[CBSE 2009, 3]

cars?

u



where the symbols have their usual meaning. (b) Use this relation to obtain the (thin) lens maker's formula. [CBSE 2004, 2008, 2009]

(b) Use the mirror formula to show that for an object, kept between the pole and focus of a concave mirror, the image appears to be formed behind the mirror. 18. Why

n1

[CBSE 2009 S]

19. Three

light rays red (R), green (G) and blue (B) are incident on a right angled prism 'abc' at face 'ab'. The refractive indices of the material of the prism for red, green and blue wavelengths are 1.39, 1.44 and 1.47 respectively. Out of the three which colour ray will emerge out of face 'ac'? Justify your answer. Trace the path of these rays after passing through face 'ab'. [CBSE 2009, 3]

25 . The

image obtained with a convex lens is erect and its length is four times the length of the object. If the focal length of the lens is 20 cm, calculate the object and image distances . [CBSE 2010, 3]

26.

A converging lens is kept coaxially in contact with a diverging lens–both the lenses being of equal focal lengths. What is the focal length of the combination? [CBSE Board 2010]







Draw a ray diagram to show the working of a compound microscope. Deduce an expression for the total magnification when the final image is formed at the near point. In a compound microscope, an object is placed at a distance of 1.5 cm from the objective of focal length 1.25 cm. If the eye piece has a focal length of 5 cm and the final image is formed at the near point, estimate the magnifying power of the microscope. [ C B S E 0 9 , 1 0 ]

34.

A ray of light is incident on one face of a glass prism and emerges out from the other face. Trace the path of the ray and derive an expression for refractive index of the glass prism. [CBSE 2011]

35.

For the same value of angle of incidence, the angle of refraction in three media A, B and C are 15°, 25°, and , 35° respectively. In which medium would the velocity of light be minimum? [CBSE 2012]

28.

Two convex lenses of focal length 20 cm and 1 cm constitute a telescope. The telescope is focussed on a point which is 1 m away from the objective. Calculate the magnification produced and the length of the tube. If the final image is formed at a distance of 25 cm from of eyepiece . [CBSE 2011, 3]

36.

Define magnifying power of a telescope. Write its expression. [CBSE 2012] A small telescope has an objective lens of focal length 150 cm and an eye piece of focal length 5 cm. If this telescope is used to view a 100 m high tower 3 km away, find the height of the mail image when it is formed 25 cm away from the eye piece.

29.

A convex lens made up of glass of refractive index 1.5 is dipped in turn, in (i) a medium of refractive index 1.65, (ii) a medium of refractive index 1.33. (a) Will it behave as a converging or a diverging lens in the two cases? (b) How will its focal length change in the two media? [CBSE 2011, 3]

37.

An object AB is kept in front of a concave mirror as shown in the figure. [CBSE 2012] (i) Complete the ray diagram showing the image formation of the object. (ii) How will the position and intensity of the image be affected if the lower half of the mirror's reflecting surface is painted black ?

27.

30. Use

the mirror equation to show that (a) an object placed between f and 2f of a concave mirror produces a real image beyond 2f. (b) a convex mirror always produces a virtual image independent of the location of the object. (c) an object placed between the pole and focus of a concave mirror produces a virtual and enlarged image. [CBSE 2011]

31.

38. You are given

three lenses L 1, L2 and L 3 each of focal length 20cm. An object is kept at 40 cm in front of L1,, as shown. The final real image is formed at the focus 'I' of L3. Find the separations between L 1, L2 and L 3.

A compound compound microscope uses an object lens of focal length 4 cm and eyepiece lens of focal length 10 cm. A n object is placed at 6 cm from the objective lens. Calculate the magnifying power of the compound microscope. Also calculate the length of the microscope. [CBSE 2011] giant refracting telescope at an observatory has an objective lens of focal length 15 m. If an eyepiece lens of focal length 1.0 cm is used, find the angular magnification of the telescope. If this telescope is used to view the moon, what is the diameter of the image of the moon formed by the objective lens? The diameter of the moon is 3.42 × 10 6 m and the radius of the lunar orbit is 3.8 × 10 8 m. [CBSE 2011]

[CBSE 2012]

32. A

33.

39.

Draw a ray diagram of a reflecting type telescope. Sate two advantages of this telescope over a refracting telescope. [CBSE 2008, 2012]

A beam of light converges at a point P. A concave lens of focal length 16 cm is placed in the path of this beam 12 cm from P. Draw a ray diagram and find the location of the point at which the beam would now converge. [CBSE 2011]







Deduce the ratio of intensity of maxima and minima in the interference pattern?

WAVE OPTICS Very Short Answer Type Questions: 1.

What is the Brewster angle for air to glass transition? ( g = 3

2. 3.

4. 5. 6. 7. 8. 9. 10.

[01 Mark Each]

What is the shape of the wave front when light is diverging from a point source? A light wave enters from air to glass. How will the following be affected? (i) Energy of the wave (ii) Frequency of the wave Draw a diagram to show cylindrical wave front? State the conditions that must be satisfied for two light sources to be coherent? In young‟s double slit experiment. The distance between the slits is halved, what change in the fringe width will take place? State the the conditions conditions which which must must be satisfied for two light light sources to be coherent. Two independent independent light light sources cannot act as coherent sources. Why? No interference interference pattern pattern is detected when two coherent sources are infinitely close to one another. Why? If the path difference produced due due to interference interference of light coming out of two slits for yellow colour of light at a point on the screen be 3  /2, what will be the colour of the fringe at the point. Give reason also. difference between the two sources varies continuously?


2. 3. 4.

5. 6.

How is a wave front different from a ray? Draw the geometrical shape of the wave fronts, when (i) Light diverges from a point source, and (ii)Light emerges out of convex lens when a point source is placed at its focus.

8.

In a young‟s double slit experiment, the position of the

)

11. What happens to the interference pattern if the phase

1.

7.

[02 Marks Each]

first fringe coincides with S1 and S2 respectively. What is the wavelength of light? 9.

Draw the diagram showing intensity distribution of light on the screen for diffraction of light at a single slit. How is the width of central maxima affected on increasing the (i) Wavelength of light used (ii) Width of the slit What happens to the width of the central maxima if the whole apparatus is immersed in water and why?

10. What

two main changes in diffraction pattern of single slit will you observe when the monochromatic source of light is replaced by a source of white light?

11.

Explain with reason, how the resolving power of a compound microscope will change when (i) frequency of the incident light on the objective lens is increased. (ii) Focal length of the objective lens is increased, and (iii) aperture of the objective lens is increased.

In Young‟s double slit experiment how is the fringe

width change when (a) Light of smaller frequency is used (b) Distance between the slits is decreased? Write two points of difference between interference and diffraction? Obtain an expression for the ration of intensities at maxima and minima in an interference pattern. A slit is illuminated by a monochromatic source of light to give two coherent sources P 1 and P2 these give bright and dark bands on a screen. At a point R, on the screen, there is a dark fringe. What relation must exist between the lengths P 1 R and P 2R? Can white light produce interference? What is the nature? (a) Derive expression for the fringe width in young‟s

double slit experiment? (b) If the two slits in young‟s double slit experiment

have width ratio 4:1,

12. The

critical angle between a given transparent medium and air is denoted by i c, A ray of light in air medium enters this transparent medium at an angle of incidence equal to the polarizing angle(i p). Deduce a relation for the angle of refraction (r p) in terms of i c .

Long Answer Type Questions: [05 Mark Each] 13. Using

Huygens‟s principle deduce the laws of

refraction? 14. (a) Coloured spectrum is seen, when we look through a muslin cloth. Why? (b) What changes in diffraction pattern of a single slit will you observe when the monochromatic source of light is replaced by a source of white light? 15. State Brewster law? Using this law prove that at the polarizing angle of incidence, the reflected and transmitted rays are perpendicular to each other?







In a single slit experiment, how the angular width of central bright fringe is maximum changed when (1) The slit width increased (2) The distance between the slit and the screen is increased. (3) Light of smaller wavelength is used.

1.

Huygen‟s principle for constructing wave fronts? (b) Using Huygen‟s principle deduce the laws of reflection of light? (c) What changes in diffraction pattern of a single slit will you observe, when the monochromatic source of light is replaced by a source of white light?

2.

CBSE PROBLEMS

90º to each other and the intensity of transmitted light is zero. What will be the intensity of transmitted light when one more polaroid is placed between these two bisecting the angle between them? Take intensity of unpolarised light as I 0. (CBSE 2005-06)

In a young‟s double slit experiment, the slit are

2.

Two Sources of Intensity I and 4I are used in an interference experiment. Find the intensity at points where the waves from two sources superimpose with a phase difference (i) zero (ii) π /2 (iii) π.

3.

In a two slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance D from the slits. If the screen is moved 5 x 10 -2 m towards the slits, the charge in fringe width is 3 x 10 5 m. If the distance between the slit is 10 -3 m. calculate the wavelength of the light used.

4.

What is meant by a linearly polarised polarised light? Which type of waves can be polarised? Briefly explain a method for producing polarised light. Two Polaroid‟s are placed at

NUMERICAL QUESTIONS

separated by 0.24 mm. The screen is 1.2m away from the slits. The fringe width is 0.3 cm calculate the wavelength of light used in the experiment?

(a) Using Huygen‟s principle draw a diagram to show

propagation of a wave front originating from a monochromatic source. (CBSE 2005) (b) Describe diffraction of light due to a single slit. Explain formation of a pattern of fringes obtained on the screen and plot showing variation of intensity with angle q in single slit diffraction.

17. (a) State

1.

(LAST 10 YEARS)

3.

(a) Light, from a sodium lamp, is passed through through two two polaroid sheets, P 1 and P2 kept one after the other. Keeping P1 fixed, P, is rotated so that its 'pass-axis' can be at different angles, q, with respect to the pass-axis of P1. [CBSE 2008] An experimentalist records the following data for the intensity of light coming out of P 2 as a function of the angle q. S.No.

1

2

 ( Angle between 0º 30º the pass  axis of

3

4

45º

5

60º 90º

the the polaroids I (Intensity of

I0 2

3 I0 8

1 2 2

I0

I0 8

0

light co min g

A narrow monochromatic beam of light of intensity I is incident a glass plate. Another identical glass plate is kept close to the first one and parallel to it. Each plate reflects 25% of the incident light and transmits the reaming. Calculate the ratio of minimum and maximum intensity in the interference pattern formed by the two beams obtained after reflection from each plate.

out of P2 )

[I0 = Intensity of beam falling on P 1] One of these observations is not in agreement with the expected theoretical variation of I. Identify this observation and write the correct expression. (b) Define Brewster angle and write the expression for it in terms of the refractive index of the medium. 4.

What is is plane polarised light? Two polaroid‟s are

placed at 90º to each other and the transmitted intensity is zero. What happens when one more Polaroid is placed between these two, bisecting the angle between them? How will the intensity of transmitted light vary on further rotating the third Polaroid? (b) If a light beam shows no intensity variation when transmitted through a Polaroid which is rotated, does it mean that the light is un-polarised? Explain briefly. (CBSE 2008)







orientations will the transmitted intensity be (i) minimum and (ii) maximum?

State the essential condition for diffraction of light to take place. Use Huygens‟ principle to explain

diffraction of light due to a narrow single slit and the formation of a pattern of fringes obtained on the screen. Sketch the pattern of fringes formed due to diffraction at a single slit showing variation of intensity with angle q. (CBSE 2007) OR What are coherent sources of light? Why are coherent sources required to obtain sustained interference pattern? 6.

10.

The diagram, given below, shows the refraction of a plane wave front, incident on the surface PP‟

separating two media, (1) and (2). Which of the two media is the rarer one? [CBSE 2009]

How is a wave front defined? Using Huygen‟s

construction draw a figure showing the propagation of a plane wave refracting at a plane surface separating two media. Hence verify Snell‟s law of refraction. (2006) 7.

8.

In a Young's Young's double slit experiment, the two slits are kept 2 mm apart and the screen is positioned 140 cm away from the plane of the slits. The slits are illuminated with light of wavelength 600 nm. Find the distance of the third bright fringe, from the central maximum, in the interference pattern obtained on the screen. If the wavelength of the incident light were changed to 480 nm, find out the shift in the position of third bright fringe from the central maximum. [CBSE 2008]

In a single slit diffraction experiment when a tiny circular obstacle is placed in the path of light from a distant source, a bright spot is seen at the centre of the shadow of the obstacle. Explain why [CBSE 2009] State two points of difference between the interference patterns obtained in Young‟s double slit experiment

and the diffraction pattern due to a single slit. 12.

How does an unpolarised light get polarised when passed through a Polaroid? [CBSE 2010] Two Polaroids are set in crossed positions. A third Polaroid is placed between the two making an angle q with the pass axis of the first Polaroid. Write the expression for the intensity of light transmitted from the second Polaroid. Write the expression for the intensity of light transmitted from the second Polaroid. In what

How would the angular separation of interference fringes in Young‟s double slit experiment change when

the distance between the slits and screen is halved? [CBSE 2009]

13. In young‟s double slit experiment, the two slits 0.15

mm apart are illuminated by monochromatic light of wavelength 450 nm. The screen is 1.0 m away from the slits. (a) Find the distance of the second (i) (i) bright fringe (ii) dark fringe from the central maximum. (b) How will the fringe pattern charge if the screen is moved away from the slits ? [CBSE 2010]

In Young‟s double slit experiment, monochromatic light

of wavelength 630 nm illuminates the pair of slits and produces an interference pattern in which two consecutive bright fringes are separated by 8.1 mm. Another source of monochromatic light produces the interference pattern in which the two consecutive bright fringes are separated by 7.2 mm,. Find the wavelength of light from the second source. [CBSE 2009] What is the effect to on the interference fringes if the monochromatic source is replaced by a source of white light? 9.

11.

14.

State Huygens' principle of diffraction of light.

[2011]

15.

State the importance of coherent sources in the phenomenon of interference. In Young's double slit experiment to produce interference pattern obtain the conditions for constructive and destructive interference. Hence deduce the expression for the fringe width. How does the fringe width get affected, if the entire experimental apparatus of Young's is immersed in water? [CBSE 2011] 16. Using Huygens' geometrical construction of wave fronts, show how a plane wave gets reflected by a reflecting surface. Hence verify laws of reflection. [CBSE 2011]

17.

(a) Define a wave front. Use Huygen ‟s principle to show diagrammatically the propagation of a plane wave front from the instant t 1 = 0 to a later time t 2. [CBSE 2011]

(b) State briefly two features which can distinguish the characteristic features of an interference pattern from those observed in the diffraction pattern due to a single slit.







(a) Why are coherent sources necessary to produce a sustained interference pattern ? (b) In Young‟s double slit ex periment using monochromatic light of wavelength l,the intensity of light at a point on the screen where path difference is l, is K units. Find out the intensity of light at a point where 2  path difference is . [CBSE 2012] 3

19.

DUAL NATURE OF MATTER AND RADIATION Very Short Answer Type Questions:

Electrons are emitted from a photosensitive surface when it is illuminated by green light but electron emission does not take place by yellow light. Will the electrons be emitted when the surface is illuminated by: (i) red light, and (ii) (ii) blue light? Why alkali metals are most suitable for photoelectric emission? Are matter waves electromagnetic? Write de-Broglie wave equation. What is the significance of negative energy of electron in an orbit? Can a hydrogen atom absorb a photon whose energy exceeds its binding energy? What is the shortest wavelength present in the Paschen series of spectral lines? The ground state energy of hydrogen atom is –13.6 eV. What are the kinetic and potential energies of the electron in this state ? Show that the speed of an electron in the innermost orbit of H-atom is 1/137 times the speed of light in vacuum. Determine the speed of the electron in n = 3 orbit of He + ion.

1.

2.

(a) In Young's double slit experiment, derive the condition for (i) constructive interference and (ii) destructive interference at a point on the screen. (b) A beam of light consisting of two wavelengths, 800 nm and 600 is used to obtain the interference fringes in a Young's double slit experiment on a screen placed 1.4 m away. If the two slits are separated by 0.28mm, calculate the least distance from the central bright maximum where the bright fringes of the two wavelengths coincide. [CBSE 2012]

3. 4. 5. 6. 7.

OR

(a) How does an unpolarized light incident on a Polaroid get polarized? Describe briefly, with the help of a necessary diagram, the polarization of light by reflection from a transparent medium. (b) Two Polaroids 'A' and 'B' are kept in crossed position. How should a third Polaroid 'C' be placed between them so that intensity of polarized light transmitted by Polaroid B reduces to 1/8 th of the intensity of unpolarized light incident on A? 20.

Which of the following waves can be polarized (i) Heat (ii) Sound waves? Give reason to support your answer.

8. 9.


(a) In what way is diffraction from each slit related to the interference pattern in a double slit experiment? (b) Two wavelengths of sodium light 590 nm and 596 nm are used, in turn to study the diffraction taking place at a single slit of aperture 2 x 10 – 4 m. The distance between the slit and the screen is 1.5 m. Calculate the separation between the positions of the first maxima of the diffraction pattern obtained in the two cases. [CBSE 2013]

[02 Marks Each]

10.

What is meant by work function of a metal ? How does the value of work function influence the kinetic energy of electrons liberated during photoelectric emission ?

11.

Define the terms 'threshold frequency' and 'stopping potential' for photoelectric effect. Show graphically how the stopping potential, for a given metal, varies with frequency of the incident radiations. Mark threshold frequency on this graph.

12.

Explain laws of photoelectric emission on the basis of Einstein's photoelectric equation.

13.

Work functions of three elements A, B and C are as given below: A: 5.0 EV, B: 3.8 eV, C: 2.8 eV. A radiation of wavelength 4125 Å is made to be incident on each of these elements. By appropriate calculations show in which case photoelectrons will not be emitted.

14.

A monochromatic beam of electromagnetic waves is incident on the cathode of a photocell. Depict graphically, how the following varies with change in frequency of incident radiation: (at constant intensity) (i) Number of electrons emitted (ii) Kinetic energy of electrons emitted (iii) The stopping potential.

[CBSE - 2013]

21.

[01 Mark Each]






16.


A source of light l ight of frequency v > v0 is placed at 2 m from the cathode of a photocell. The stopping potential is found to be V 0. If the distance of the light source is halved, state with reason what changes occur in (i) Stopping potential (ii) Photoelectric current, and (iii) Maximum velocity of photoelectrons emitted. Define the term: with reference to Photoelectric effect. (a) (i) Work function, (ii) Threshold frequency and (iii) Stopping potential, (b) Calculate the maximum kinetic energy of electrons emitted from a photosensitive surface of work function 3.2 eV, for the incident radiation of wavelength 300 nm.

CBSE PROBLEMS

Mention the significance of Davisson-Germer experiment. An a-particle and a proton are accelerated from rest through the same potential difference V. Find the ratio of de-Broglie wavelengths associated with them. [CBSE 2005]

7.

de Broglie wavelength associated with an electron accelerated through a potential difference V is l. What will be its wavelength wave length when the accelerating potential is increased to 4 V? [CBSE 2006]

8.

A hydrogen atom initially in the ground level lev el absorbs a photon; which excites it to the n = 4 level. Determine the wavelength and frequency of photon . [CBSE 2006]

9.

Ultraviolet radiations of different frequencies u 1 and u2 are incident on two photosensitive materials having work functions W 1 and W2 (W1 > W2) respectively. The kinetic energy of the emitted electrons is same in both the cases. Which one of the two radiations will be of higher frequency ? [CBSE 2007]

10.

Draw a schematic diagram of the experimental arrangement used by. Davisson and Germer to establish the wave nature of electrons. Explain briefly how the de-Broglie wave relation experimentally verified in case of electrons. [CBSE 2003, 2007]

11.

Two lines A and B, in the plot given below show the variation of de Broglie wavelength, l ve v e rs u s V , where V is the accelerating potential difference, for two particles carrying the same charge. Which one of two represents a particle of smaller mass? [CBSE 2008]

12.

The following graph shows the variation of stopping potential V 0 with the frequency u of the incident radiation for two photosensitive metals X and Y

(LAST 10 YEARS)

1.

Write any two applications of X-rays.

2.

Why are de-Broglie waves associated with a moving football not visible ? The wavelength l, of a photon and the de-Broglie wavelength, of an electron have the same value. Show that the energy of the photon is 2 mc times the kinetic energy of the electron, where h m, c and h have their usual meanings. [CBSE 2003]

3.

6.

[CBSE 2003]

Red light, however bright it is, cannot produce the emission electrons from a clean zinc surface. But even weak ultraviolet radiation can do so. Why? [CBSE 2004] X-rays of wavelength „ l‟ fall on photosensitive surface, emitting electrons. Assuming that the work function of the surface can be neglected, prove that the de-Broglie wavelength of electrons emitted will be

h 2mc

.

[CBSE 2004]

4.

Define the term 'work function' of a metal. The threshold frequency of a metal is f 0. When the light of frequency 2f 0 is incident on the metal plate, the maximum velocity of electrons emitted is v 1. When the frequency of the incident radiation radiation is increased to 5f 0, the maximum velocity of electrons emitted is v 2. Find the ratio of v 1 to v2. [CBSE 2004]

5.

Ultraviolet light is incident on two photosensitive materials having work function W 1 and W2 (W1 > W2). In which case will the kinetic energy of the emitted electrons be greater? Why? [CBSE 2005]

(i) Which of the metals has larger threshold wavelength ? Give reason. [CBSE 2008]







(ii) Explain, giving reason, which metal gives out electrons, having larger kinetic energy, for the same wavelength of the incident radiation. (iii) If the distance between the light source and metal X is halved, how will the kinetic energy of electrons emitted from it change ? Give reason. 13.

The ground state energy of hydrogen atom is –13.6 eV. (i)What is the kinetic energy of an electron in the 2nd excited state? (ii)If the electron jumps to the ground state from the 2nd excited state, calculate the wavelength of the spectral line emitted. [CBSE 2008]

14.

The stopping potential in an experiment on photoelectric effect is 1.5 V. What is the maximum kinetic energy of the photoelectrons emitted ? [CBSE 2009]

15.

Define ionisation energy. What is its value for a hydrogen atom? [CBSE 2010]

16. Write Einstein‟s photoelectric equation. State clearly

any two salient features observe in photoelectric effect, which can be explained on the basis of the above equation. [CBSE 2010] 17

Deduce the expression for the magnetic dipole moment of an electron orbiting around the central nucleus. [CBSE 2010]

18. Define the term „stopping potential‟ in relation to

photoelectric effect.

[CBSE 2011]

19. (a) Using de Broglie‟s hypothesis, explain with the help

of a suitabl e diagram, Bohr‟s second postulate of quantization of energy levels in a hydrogen atom. (b) The ground state energy of hydrogen atom is –13.6 eV. What are the kinetic and potential energies of the electron in this state? [CBSE 2011] 20.

A proton and an electron have same kinetic energy. Which one has greater de-Broglie wavelength and why? [CBSE 2012]

21. Define the terms (i) „cut -off voltage‟ and (ii) „threshold

frequency‟

in

relation

to

the

phenomenon

of

photoelectric effect. Using Einstein‟s photoelectric equations shows how the

cut-off voltage and threshold frequency for a given photosensitive material can be determined with the help of a suitable plot/graph. [CBSE - 2006, 2012] 22.

(a) In a typical nuclear reaction, [CBSE 2013] 2 2 3 1 1 H 1 H 2 He  0 n  3.27 MeV ,

although number of nucleons is conserved, yet energy is released. How? Explain. (b) Show that nuclear density in a given nucleus is independent of mass number A 23. Using Bohr‟s postulates, obtain the expression for the

total energy of the electron in the stationary states of the hydrogen atom. Hence draw the energy level diagram showing how the line spectra corresponding to Balmer series occur due to transition between energy levels. [CBSE 2013]

NUCLIE, NUCLEAR FORCE Very Short Answer Type Questions:

[01 Mark Each]

What do you mean by Q value of a nuclear reaction? (P.S.E.B. (P.S.E. B. 2 2000) 000) 2. How is half-life of a radioactive substance related to its average life? (P.S.E.B. 2001) 3. Arrange radioactive radiations in the order of increasing penetrating power. (CB (CBSE SE 2006) 4. Name two elementary particles which have almost infinite life time (H.C.S. (H.C.S .E. E. 2004) What is the relation between decay constant and 5. half-life of a radioactive element? 6. What fraction of tritium will remain after 25 years? Given its half-life is 12.5 years. (C.B.S.E. (C.B.S .E. 2 2001) 001) 7. The half life of a radioactive element A is same as mean life time of another radioactive element B. Initially, both have same number of atoms. B decays faster than A. Why? (P.S.E.B. (P.S.E. B. 2 2001) 001) 8. Compare the radii of two nuclei with mass numbers 1 and 27 respectively. (C.B.S.E. (C.B.S .E. 2 2000) 000) 9. What is the order of nuclear density? (P.S.E.B. (P.S.E. B. 2 2000) 000) nucleons together in a nucleus? 10 . What holds nucleons 1.

(H.B.S (H.B. S.E. .E. 2001) 2001 )

11.

Select the pairs of isobars and isotones from the following nuclei : 14 13 14 16 (H.B.S (H.B. S.E. .E. 2000) 2000 ) 6C , 7N , 7N , 8O

Select the pairs of isotopes and isotones from the following nuclei: 13 14 30 31 (H. (H.B. B.S.E. S.E. 2000) 2000 ) 6 C , 7 N , 15 P , 15 P 13 . Which one of 3 X 7 and 3 Y 4 are likely to be more stable? Give reason . (C.B.S.E (C.B.S .E.. 2000) 2000 ) 14 . Define atomic mass unit. Write its energy equivalent. 15 . Define nuclear fission. 16 . What is the ratio of kWh to MeV? 17 . What is meant meant by mass defect of a nucleus?

12.

18.



Write symbolically the  decays process of

32 15

P.







Short Answer Type Questions: [02 Marks Each] 19 .

8.

The sequence of of decay of radioactive nucleus is      D 1   D 2   D 3   D4 D  If nucleon number and atomic number of D 2 are 176 and 71 respectively, what are their val v al ue s fo r D an d D 4 ? (C.B.S.E. 2005, 2006)

9.

(a) Draw the energy level diagram showing the emission of   particles followed by   rays by a

Explain one similarity and one dissimilarity between nuclear fission and fusion. (P.S.E.B. 2005)

20 . What

are thermal neutrons? Why are neutrons considered as ideal particles for nuclear fission? (C.B.S.E. 2002)

21 . What

do you understand by binding energy per nucleon?

22.

60 27

Write any two characteristic properties of nuclear force.

24 . A

CBSE PROBLEMS 1.

10.

(LAST 10 YEARS)

When a deuteron deuteron of mass 2.0141 u and negligible kinetic energy is absorbed by a lithium  36 Li  nucleus of mass 6.0155 u, the compound nucleus disintegrates spontaneously into two alpha particles, each of mass 4.0026 u. Calculate the energy in joules carried by each  (1u = 1.66 × 10 –27 kg) (CBSE 2004)

11 . Explain

the concept of nuclear forces. Discuss their characteristic properties. Which properties distinguish them from electrostatic forces? (C.B.S.E. 2006, 2008, P.S.E.B 2001)

„Heavy water is often used as a moderator in thermal

nuclear reactors. Give reason. 3.

4.

5. 6.

7.

(CBSE 2004)

Draw the graph showing the variation of binding energy per nucleon with mass number. Give the reason for the decrease of binding energy per nucleon for nuclei with high mass numbers. (CBSE 2004)

A neutron is absorbed by a 63 Li nucleus with the subsequent emission of an alpha particle. (i) Write the corresponding nuclear reaction. (ii) Calculate the energy released, in MeV, in this reaction. (CBSE BOARD 2006) 6 [Given : mass 3 Li = 6.015126 u; mass (neutron) = 1.0086654 u mass (alpha particle) = 0.0026044 u and mass (triton) = 3.0100000 u. Take 1 u = 931 MeV/c 2]

State and explain the laws of radioactive disintegration. Hence define disintegration constant and half-life period. Establish relation between them. ( C . B . S . E . 2 0 0 6 , P . S . E . B . 2 0 0 5 , C.B.S.E.2004, H.P.B.S.E. 2004, H.B.S.E. 2001)

13.

Name the reaction which takes place when a slow 235 neutron beam strikes 92 U nuclei. Write the nuclear reaction involved. (CBSE BOARD 2003, 2005) Define decay constant (C.B.S.E.2006) Define the terms half-life period and decay constant of a radioactive substance. Write their S.I. units. Establish the relationship between the two. (CBSE 2004, 2006)

A radioactive sample contains 2.2 mg of pure 11 C 6 which has half-life period of 1224 second. Calculate (i) the number of atoms present initially. (ii) the activity when 5  g of the sample will be left . (CBSE BOARD 2005 SET -1)

12. 2.

(CBSE BOARD 2005 SET -1)

(b) Plot the distribution of kinetic energy of   particles and state why the energy spectrum is continuous.

[CBSE Out side Delhi board 2011 SET -1]

radioactive isotope has a half-life of T years. How long will it take the activity to reduce to (a) 3.125%, (b) 1% of its original value?

Co nucleus.

Draw the graph to show variation of binding energy per nucleon with mass number of different atomic nuclei. Calculate binding energy/nucleon of 40 20 Ca nucleus. Given : mas of 40 = 39.962589 u 20 Ca mass of proton = 1.007825 u mass of neutron = 1.008665 u and 1 u = 931 Me V/c 2

14.

(CBSE BOARD 2007)

Calculate the amount of energy released during the  -decay of 92238U 92034 Th  24 He Given: atomic mass of

238 92

U = 238.05079 u, atomic

234 mass of 90 Th = 234.04363 u, atomic mass 42 He = 4.00260 u, 1amu = 931.5 MeV/c 2 .Is this decay spontaneous? Given reason (CBSE BOARD 2007)






23 23 A nucleus 10 Ne undergoes   decay and becomes 11 Na. Calculate the maximum kinetic energy of electron emitted assuming that the daughter nucleus and antineutrino carry negligible kinetic energy 23  mass of 10 Ne  22.994466 u 

  23 m a s s o f N a 22.989770 u    11 1u  931.5 Me V / c 2   

16.


The mass number and atomic number of A are 180 and 72 respectively. What are these numbers for A 4? (CBSE BOARD 2006, 2007, 2009)

22.

Define the activity of a radionuclide. Write its S.I. unit. Give a plot of the activity of a radioactive species versus time. (CBSE BOARD 2009) How long will be radioactive isotope whose half-life is T years, take for its activity to reduce to 1/8 th of its initial value ?

23.

Draw a plot a potential energy of a pair of nucleons as a function function of their separation. separation. Write Write two important conclusions which you can draw regarding the nature of nuclear forces. (CBSE BOARD 2007, 2010, 2012)

(CBSE 2008)

If the nucleons of a nucleus are separated far apart from each other, the sum of masses of all these nucleons is larger than the mass of the nucleus. Where does this mass difference come from? Calculate the energy released if 238U nucleus emits an a-particle. Given: (CBSE BOARD 2007) Atomic mas of 238U = 238.0508 u Atomic mass of 234Th = 234.04363 u Atomic mass of alpha-particle = 4.00260 u and 1u = 931 MeV/c 2

24.

(CBSE BOARD 2010)

25. 17.

18 .

6

A neutron is absorbed by a 3 Li nucleus with the subsequent emission of an alpha particle. (i) Write the corresponding nuclear reaction. (ii) Calculate the energy released, in MeV, in this reaction. (CBSE BOARD 2006, 2007) 6 [Given: mass 3 Li = 6.015126 u; mass (neutron) = 1.0086654 u mass (alpha particle) = 0.0026044 u and mass (triton) = 3.0100000 u. Take i u = 931 MeV/c 2] What do you understand by isotopes, isobars and isotones? Explain with illustrations. (C.B.S.E. 2008)

19.

A nucleus

23 10

Ne undergoes   decay and becomes

State the law of radioactive decay. Plot a graph showing the number (N) of undecayed nuclei as s function of time (t) for a given radioactive sample having half life T 1/2. (CBSC 2011) Depict in the plot the number of undecayed nuclei at (i) t = 3 T 1/2 and (ii) t = 4 T 1/2. 27 . What is the effect on neutron to proton ratio in a nucleus when (i) an electron, (ii) a positron is emitted? (C.B.S.E. 2003, 2006, 2011)

28.

11

23  mass of 10 Ne  22.994466 u    23 m a s s o f N a 22.989770 u    11 1u  931.5 Me V / c 2   

20.

(CBSE BOARD 2008)

How is the size of nucleus experimentally determined? Write the relation between the radius and mass number of the nucleus. Show that the density of nucleus is independent of its mass number. (CBSE BOARD 2011)

26.

23

Na. Calculate the maximum kinetic energy of electrons emitted assuming that the daughter nucleus and anti-neutrino carry negligible kinetic energy

32 (a) Write symbolically the b – decay process of 15 P. (b) Derive an expression for the average life of a radionuclide. Give its relationship with the half-life

A nucleus undergoes   decay. How does it‟s (i) mass number (ii) atomic number change? (CBSE BOARD 2006, 2011)

29.

How is the radius of a nucleus related to its mass number?

30.

(a) Derive the law of radioactive decay, (CBSE 2011) N = N0 e–lt (b) Explain, giving necessary reactions, how energy is released during (i) fission and (ii) fusion.

Two nuclei have mass umbers in the ratio 1:2. What is the ratio of their nuclear densities (CBSE BOARD 2009)

21. A radioactive nucleus „A‟ undergoes a series of decays

according to the following scheme:     A   A1   A2   A3   A 4 QUESTION BANK FOR CLASS XII (CBSE BOARD-2017) BOARD-2017)






SEMICONDUCTOR DEVICES

Long Answer Type Questions: [05 Marks Each] 12.

With the help of a circuit diagram explain the working of a transistor as an oscillator.

How is a p-type semiconductor formed? Name Name the majority carriers in it. Draw the energy band diagram of a p-type semiconductor.

13.

Explain briefly with the help of a circuit diagram how V-I characteristics of a p-n junction diode are obtained in: (i) forward bias & (ii) reverse bias.

2.

How is an n-type semiconductor formed? formed? Name Name the the majority carriers in it. Draw the energy band diagram of a n-type semiconductor.

14.

3.

With the help of a diagram, show the biasing of a light emitting diode (LED). Give its two advantages over conventional incandescent lamps.

Explain the function of base region of a transistor. transistor. Why this region is made thin and lightly doped? Draw a circuit diagram to study the input and the output characteristics of n-p-n transistor in a common emitter (CE) configuration. Show these characteristics graphically. Explain how current amplification factor of the transistor is calculated using output characteristics.

4.

Draw a circuit diagram to show how a photodiode photodiode is biased. Draw its characteristic curves for two different illumination intensities.

15.

Draw the energy bands of p-type and n-type semiconductors. Explain with a circuit diagram the working of a full wave rectifier.

5.

Give the logic symbol for an AND gate. Draw the output wave form for input wave forms for this thi s gate.

16.

Explain with the help of a circuit diagram the use of an n-p-n transistor as an amplifier in common emitter configuration. Draw the input and output wave forms of the signal. Write the expression for its voltage gain.

17.

What is an n-p-n n-p-n transistor? How does it differ from pn-p transistor? Give their symbols. Explain transistor action.

18.

Explain the working of transistor as a switch. Draw transfer characteristic curve by showing 1) Cut-off region 2) Active region and 3) Saturation region.

Short Answer Type Questions: [02 Marks Each] 1.

Short Answer Type Questions: [03 Marks Each] 6.

What is rectification? rectification? How can a diode valve be used as half wave rectifier and full wave rectifier?

7.

Explain how the depletion layer and the barrier potential are formed in a p-n junction diode.

8.

Draw a circuit diagram for use of NPN transistor as an amplifier in common emitter configuration. The input resistance 1000Ω of a transistor is On changing its base current by 10 A, the collector current increases by 2 mA. If a load resistance of 5KΩ is used in the circuit, calculate (i) the current gain & (ii) voltage gain of the amplifier

9.

The output output of an AND gate is connected to both the inputs of a NAND gate. Draw the logic circuit of this combination of gates and write its truth table.

10.

What is a Zener diode? How it is symbolically represented? With the help of a circuit diagram, explain the use of Zener diode as a voltage stabilizer.

11.

With the help of a suitable diagram, explain the formation of depletion region in a p-n junction. How does its width change when the junction is: (i) forward biased? & (ii) reverse biased?







COMMUNICATION SYSTEM Short Answer Type Questions: [02 Marks Each] 1.

2.

3.

4.

Draw a block diagram of communication system. Distinguish between point to point and and broadcast communication modes. Give one example of each. Explain the following terms. a) Ground waves b) Space waves and and c) sky waves. What does the term LOS communication mean? Name the types of waves that are used for this communication. Give typical examples, with the help of a suitable figure, of communication systems that use space wave mode propagation.

Write the function of 1) Transducer and 2) repeater in the context of communication system. 6. What is modulation? Explain the the need of modulating a low frequency information signal. 7. We do not choose to transmit an audio signal by just directly converting it to an E.M wave of the same frequency. Give two reasons for the same. 8. Explain briefly with the help of diagrams the terms (i) amplitude modulation and (ii) Frequency modulation. Which of these (i) gives better quality transmission? (ii) Has a larger coverage 9. Why is short wave bands used for long distance transmission of signals? 10. Optical and radio telescope are built on the ground but x-ray astronomy is possible only from satellite? 11. Draw a block diagram for a transmitter transmitter and a receiver of AM wave. 12. Why is delta modulation a convenient method of digital modulation? 13. Where the two wire transmission line, Coaxial cable, Optical fibre are employed. 14. Differentiate between (i) PAM PAM and (II) PPM . 15. An audio signal of 1 kHz is used to modulate a carrier of 500 kHz. Determine (i) Sideband frequency (ii) Bandwidth required. 5.

16. The

antenna current of an AM transmitter is 8A when only carrier is sent but it increases to 8.93A when the carrier is sinusoid ally modulated. Find the percentage modulation index. 17. Frequencies higher than 10MHz are found not to be reflected by the ionosphere on a particular day at a place. Calculate the maximum electron density of the ionosphere. 18. You are given three semiconductors A, B, C with respective band gaps of 3eV, 2eV and 1eV for use in a photo detector to detect λ = 1400nm. Select the suitable semiconductor. Give reasons.

Long Answer Type Type Questions: [05 Marks Each] 19.

Define the term term modulation index for an AM wave. What What would be the modulation index index for an AM wave for which the maximum amplitude is „a‟ and the minimum amplitude is b‟

20. A TV tower has a height „h‟. Derive an expression for

maximum distance up to which the signal can be received from the earth. 21. What

is meant by the term modulation? Explain with the help of a block diagram, how the process of modulation is carried out in AM broadcasts?

22. What is meant by „production‟ of a modulated carrier wave?

Describe briefly the essential steps with block diagram production. 23. What is meant by „detection‟ of a modulated carrier wave?

Describe briefly the essential steps with block diagram detection. 24. A schematic arrangement for transmitting a message signal signal (20 Hz to 20 kHz) is given below:

Give two drawbacks from which this arrangement suffers. Describe briefly with the help of a block diagram the alternative arrangement for the transmission and reception of the message signal. 25.

Ground receiver station is receiving receiving a signal at (i) 5MH and (ii 100MHz transmitted from a round transmitter at a height of 300 m, located at a distance of 100 km from the receiver station. Identify whether the signal is coming via space wave or sky wave propagation or satellite transponder. Radius of earth = 6.4 x 10 6 m N max of the Iso sphere = 10 12 m3

26.

An AM wave is represented by the expression: v = 5(1+0.6cos 6280t) 6280t) sin 221 X 10 4t volts (i) What are the maximum and minimum amplitudes of the AM wave? (ii) What frequency components are contained in the modulated wave?




PHYSICS QUESTIONBANK 2017 XIIth CBSE BOARD EXAM

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