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Question 1C
You are to plan an investigation of how the magnetic field strength varies along the axis of a solenoid. You are then to analyse a set of data from such an experiment. (a) (i) A solenoid is set up as shown in the diagram below. below. Add to the diagram the circuit you would connect to the solenoid to set and maintain a known value of current in the solenoid.
C
x Ax i is s
(3)
(ii) Draw how you would place a Hall probe to measure the magnetic field strength at a point along the axis a distance x from the centre C of the solenoid. You should draw the Hall probe outside the solenoid and should take care to show the orientation of the chip (sensor) correctly. (1) (iii) Describe how you would determine the distance x. x. You may add to the diagram if you wish.
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(b) The solenoid has a length length of 276 mm and has 337 turns. turns. When the current in the solenoid was adjusted to 500 mA, the calibrated Hall probe indicated that the magnetic field strength at the centre of the solenoid was 0.761 mT. mT. The magnetic field strength B strength B at the centre of a solenoid having n turns per metre is given by: B = µ0 n I when the current in the solenoid is I is I . Discuss the extent to which you think that the Hall probe is correctly calibrated. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. (3) (c) The following data were obtained when the magnetic field strength B strength B was measured along the axis at different distances x from the centre of the solenoid, keeping the current current constant constant at 500 mA. x / mm
B / mT
0
0.761
40
0.760
80
0.706 Sign up to vote on this title
120
0.549 Useful
140
0.330
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QUESTION 1C CONTINUES ON THE NEXT PAGE
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(d) Theory suggests that the magnetic field strength at the end of a long solenoid is exactly half that at its centre. centre. Discuss the extent to which this experiment experiment supports this suggestion. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. (3) (Total 16 marks) TOTAL FOR PAPER: 48 MARKS
END
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Question 2C
You are to plan an investigation of how the magnetic field strength varies along the axis of a coil. You are then to analyse a set of data from such an experiment. (a) (i) A flat circular circular coil is set up as shown in the diagram below. below. Add to the diagram the circuit you would connect to the coil to set and maintain a known value of current in the coil.
x
Axis
C
(3)
(ii) Draw how you would place a Hall probe to to measure the magnetic field strength at a point along the axis a distance x distance x from the centre C of the coil. You should be careful to show the orientation of the Hall chip (sensor) correctly. (1)
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(iii) Describe how you would determine the average diameter of the coil. You may Useful Not useful add to the diagram if you wish. ........................... ........................................ ........................... ............................ ........................... ........................... ........................... ........................... .................... ......
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(b) The coil has a diameter of 124 mm and has 70 turns. turns. When the current in the coil was adjusted to 500 mA, the calibrated Hall probe probe indicated that the magnetic field strength at the centre of the the coil was 0.350 mT. mT. The magnetic field strength B strength B at the centre of a coil having a radius r and turns is r and N N turns given by B
=
µ 0 NI
2r
when the current in the coil is I. is I. Discuss the extent to which you think that the Hall probe is correctly calibrated. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. (3) (c) The following data were obtained when the magnetic field strength B strength B was measured along the axis at different distances x distances x from the centre of the coil, keeping the current constant constant at 500 mA. x / mm
B / mT
0
0.350
20
0.304
40
0.219
50
0.163
60
0.120
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QUESTION 2C CONTINUES ON THE NEXT PAGE
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(d) Theory suggests that when x = r , the radius of the coil, the magnetic field strength is 1/ 8 of the the fiel field d stren strength gth at the the cent centre re of of the the coil. coil. Discus Discusss the the exten extentt to which this experiment supports this suggestion. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. (3) (Total 16 marks) TOTAL FOR PAPER: 48 MARKS END
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Question C
You are to plan an investigation into the relationship between the frequency of vibration of a rubber cord and the tension in the cord when it is made to resonate. You are then to analyse a set of data from such an experiment. (a) When a stationary (standing) (standing) wave in the fundamental mode is formed on a length l of rubber cord there is one antinode. antinode. Draw below the shape of this this oscillation.
l State the relationship between the wavelength λ of the wave and the length l between l between the supports. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. (2) (b) Stationary waves in a fixed length of a horizontal rubber cord under tension can be produced using a vibration transducer and a signal generator. (i) Draw below a diagram of the experimental arrangement you would use to to display such standing waves. The following additional apparatus is available: • •
slotted masses and hanger to provide the tension; pulley mounted on a clamp.
Mark on your diagram the fixed length l .
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(ii) Describe the readings you would take to investigate the relationship between the tension T in the cord and the fundamental resonant frequency f for a fixed length l . ........................... ........................................ ........................... ............................ ........................... ........................... ........................... ........................... .................... ...... ........................... ........................................ ........................... ............................ ........................... ........................... ........................... ........................... .................... ...... ........................... ........................................ ........................... ............................ ........................... ........................... ........................... ........................... .................... ...... ........................... ........................................ ........................... ............................ ........................... ........................... ........................... ........................... .................... ...... ........................... ........................................ ........................... ............................ ........................... ........................... ........................... ........................... .................... ...... (2) (iii) The resonant frequency f frequency f is is related to the tension T in T in a cord of fixed length l by l by the equation T = k l 2 f 2 where k is k is a constant. Explain clearly why a graph of ln T against ln f will will produce a straight line. T against ln f ........................... ........................................ ........................... ............................ ........................... ........................... ........................... ........................... .................... ...... ........................... ........................................ ........................... ............................ ........................... ........................... ........................... ........................... .................... ...... (2) (c) Such an experiment produced the following data: T / T / N
f / f / Hz
0.70
10.2
1.20
13.5
1.70
16.3
2.20
18.8
2.70
21.0
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(4)
(d) Determine a value for the gradient of your graph.
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Question C
A music amplifier can be thought of as a source of emf with an internal resistance. resistance. When such an amplifier is connected to a load resistance such as a loudspeaker, the power developed in the loudspeaker varies with the resistance of the loudspeaker. loudspeaker. You are to plan an experiment to measure how the power varies with the resistance and then to analyse some data. Amplifier E
r
V R Load resistance (a) (i) Explain why, why, when the switch is open, the reading on the voltmeter is very close to the emf E of amplifier. E of the amplifier. ........................... ........................................ ........................... ............................ ........................... ........................... ........................... ........................... .................... ...... ........................... ........................................ ........................... ............................ ........................... ........................... ........................... ........................... .................... ...... ........................... ........................................ ........................... ............................ ........................... ........................... ........................... ........................... .................... ...... (ii) The switch is now closed. Explain why the reading V on V on the voltmeter falls. ........................... ........................................ ........................... ............................ ........................... ........................... ........................... ........................... .................... ...... ........................... ........................................ ........................... ............................ ........................... ........................... ........................... ........................... .................... ...... ........................... ........................................ ........................... ............................ ........................... ........................... ........................... ........................... .................... ......
(iii) For a given value of R of R state an expression you would use to calculate the value Sign up to vote on this title of the current in the the circuit. Hence show that the internal resistance r of the Useful Not useful amplifier is given by.
E r = R − 1
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(b) Describe how you would investigate how the power developed in the load varies with with its resistance R resistance R.. You should say what readings you would take and how you would obtain your values of the power. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. (3) (c) For a certain amplifier the following following data were obtained. R / Ω
V / V / V
4.0
8.33
5.0
9.62
7.0
11.67
9.0
13.24
11.0
14.47
13.0
15.48
On the grid opposite plot a graph of power P power P against resistance R resistance R.. You should add any processed data to the table. From your graph find the value of the maximum power P power P m in the load and the resistance R resistance Rm that produces maximum power. Sign up to vote on this title
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(5)
P m and R (d) Use your your values of P and Rm to find the terminal potential difference V m, across the resistor at maximum power. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. (1)
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(e) Hence find a value for the internal internal resistance of the amplifier given that its emf is 25 V. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. Calculate the efficiency of the energy transfer from the amplifier to the loudspeaker when it is working at maximum power. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. ........................... ......................................... ........................... ........................... ........................... ........................... ............................ ........................... .......................... ............. (2) (Total 16 marks) TOTAL FOR PAPER: 48 MARKS END
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Question 1C
You are to plan an experiment on a sample of gas using computer technology to capture the data. You will then analyse a set of data from from a similar experiment. (a) A sample of gas is held in a container at constant volume. The pressure of the gas is monitored by a pressure sensor mounted through the top of the container. container. The temperature of the gas is varied by placing the container in a water bath and the temperature of the bath is monitored by a temperature temperature sensor. The output from each sensor is sent to a computer to record the data. Draw a block diagram to show how the data is fed to the computer.
The temperature is to be varied from the ice point to the boiling point of the water. How should the computer be used to record an appropriate set of data for this experiment? ....................................................................................................................................... .......................................................................................................................................
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....................................................................................................................................... Useful Not useful Suggest two experimental precautions that you would take to ensure that the data are accurate.
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(b) By considering the Ideal Gas Equation pV = pV = nRT explain why a graph of p p against T will T will be a straight line through the origin. ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... Write down the expression for the gradient of such a graph. ....................................................................................................................................... (4) (c) In such an experiment experiment the following data were recorded. recorded. θ /
°C
p / kPa
0
101
10
105
22
110
37
115
47
118
61
124
75
129
87
133
100
138
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p against T on T on the grid opposite. Use the additional column for any Plot a graph of p processed data.
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(d) Determine the gradient gradient of your graph. ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... Given that the volume of the container is 500 cm3, use your value for the gradient to calculate the number of moles of gas in the container. ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... (4)
Q1C
(Total 16 marks) TOTAL FOR PAPER: 48 MARKS
END
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Question 2C
You are to plan an experiment on a sample of gas using computer technology to capture the data. You will then analyse a set of data from from a similar experiment. (a) A calibrated calibrated syringe is filled filled with the gas at atmospheric atmospheric pressure. The pressure of the gas is monitored by a pressure sensor attached to the end of the syringe. This sensor measures the difference between the pressure of the gas and atmospheric pressure. The output from this sensor is sent to a computer to record the data. The block diagram for measuring and recording the pressure sensor is shown below:
Sensor
Interface data logger
Computer
The method is to vary the volume of the gas whilst keeping the temperature constant. The computer records the sensor reading. reading. The volume of the gas is read from the scale on the syringe and the values are entered manually using the keyboard. What must be done to avoid a systematic error in the pressure of the gas? ....................................................................................................................................... ....................................................................................................................................... Suggest two experimental precautions that you would take to ensure that the data are accurate. ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... Suggest an advantage of using computer technology for this experiment.
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(b) By considering the Ideal Gas Equation pV = nRT explain why a graph of p p against 1/V 1/V will will be a straight line through the origin. ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... Write down the expression for the gradient of such a graph. ....................................................................................................................................... (3) (c) In such an experiment experiment the following data were recorded. recorded. p / kPa
V / V / cm3
101
60.0
112
54.0
120
50.2
135
45.0
150
40.2
167
36.5
179
34.0
190
32.0
200
29.9
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p against 1/V Plot a graph of p 1/V on on the grid opposite. Use the additional column for any processed data.
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(4)
(d) Determine the gradient gradient of your graph. ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... Given that the temperature of the room is 25 °C, calculate the number of moles of gas in the container. .......................................................................................................................................
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Question C
You are to plan an investigation of how the resistance of a thermistor varies with temperature. You are then to analyse a set of data from such an experiment. (a) (i) Draw a diagram of the arrangement you would use to measure measure the resistance of a thermistor at different temperatures in the range 10 °C to 70 °C.
(3)
(ii) Describe how you would carry out the experiment and state any precautions that you would take to improve the accuracy of your results. ................................................................................................................................ ................................................................................................................................ ................................................................................................................................ ................................................................................................................................ Sign up to vote on this title
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(b) A student suggests that the resistance resistance R R of a thermistor may be related to its celsius temperature θ by by an equation of the form R = R0 e – aθ where R where R0 is the resistance at 0 C and a is a constant. °
R0 and the Explain how a graph of ln R ln R against θ would enable you to find values for R constant a. ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... (2) (c) The following data were obtained in such an experiment. θ /
°C
R / k Ω
10.0
11.54
20.0
7.50
30.0
4.76
40.0
3.16
50.0
2.05
60.0
1.21
70.0
0.67
Add values of ln R ln R to the table and then plot a graph of ln R ln R against opposite.
θ on
the grid
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(d) (i) Over what range of temperatures do the results of this experiment suggest that the proposed equation is correct? ................................................................................................................................ (ii) Use your graph to estimate a value for R for R0, the resistance of the thermistor at 0 C. °
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Question C
You are to plan an investigation of how the bending of a beam, when a mass is hung from the end of the beam, varies with the length of the beam. You are then to analyse a set of data from such an experiment.
(a) The beam, in the form of a wooden wooden metre rule, is clamped over the end of a bench as shown below, with with a 500 g mass suspended from its end.
It is suggested that the depression y depression y of the end of the rule m ay vary with the horizontal distance x distance x according to the equation y = kxn k and n are constants. where k and The distance x distance x is measured from the point at which the rule is clamped to the centre of gravity of the suspended mass. Describe exactly how you would measure the quantities x quantities x and y and y.. You may add to the diagram if you wish. ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... Sign up to vote on this title
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(b) Explain how a graph of ln y ln y against ln x ln x would enable you to determine the constants k and k and n. ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... (2) (c) The following data were obtained in such an experiment. x / mm / mm
y / mm / mm
900
190
800
121
700
90
600
52
500
31
400
16
Add values of ln x ln x and ln y ln y to the table and then plot a graph of ln y against ln x ln x on the grid opposite.
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(d) Use your graph to determine a value for the constant n. ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... (2) (e) The constant k depends k depends on the width a and the thickness b of the metre rule. Describe how you would make accurate measurements of each of these quantities. ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... (3)
