Lab Report for circuit theory

EE 1002 CIRCUIT THEORY LAB REPORT

Contents

1.

2.

LAB 1: Ohm’s Law ................................................................................................................... 3 1.1

AIM: AIM: ................................................................................................................................... 3

1.2

APPARATUS: APPARATUS: ................................................................................................................... 3

1.3

CIRCUIT DIAGRAM: ..................................................................................................... DIAGRAM: ..................................................................................................... 3

1.4

METHODOLOGY: METHODOLOGY: .......................................................................................................... 4

1.5

RESULTS: RESULTS: ......................................................................................................................... 5

1.6

DISCUSSION:................................................................................................................... DISCUSSION:................................................................................................................... 6

1.7

CONCLUSION: CONCLUSION: ................................................................................................................ 8

LAB 2: Voltage Division ........................................................................................................... Division ........................................................................................................... 9 2.1

AIM: AIM: ................................................................................................................................... 9

2.2

APPARATUS: APPARATUS: ................................................................................................................... 9

2.3

CIRCUIT DIAGRAM: ................................................................................................... DIAGRAM: ................................................................................................... 10

2.4

METHODOLOGY: METHODOLOGY: ........................................................................................................ 11

2.5

RESULTS: RESULTS: ....................................................................................................................... 12

2.6

DISCUSSION:................................................................................................................. DISCUSSION:................................................................................................................. 13

2.7

CONCLUSION: CONCLUSION: .............................................................................................................. 14

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4.

5.

UEL ID: U1060761

LAB 3: Superposition Theorem............................................................................................. Theorem............................................................................................. 15 3.1

AIM: AIM: ................................................................................................................................. 15

3.2

APPARATUS: APPARATUS: ................................................................................................................. 15

3.3


3.4


3.5

RESULTS: RESULTS: ....................................................................................................................... 18

3.6


3.7


LAB 4: Thevenin’s Equivalent Circuit ................................................................................. 22 4.1

AIM: AIM: ................................................................................................................................. 22

4.2

APPARATUS: APPARATUS: ................................................................................................................. 22

4.3


4.4


4.4.1

Method A (Open circuit test and a load test) ....................................................... test) ....................................................... 23

4.4.2

Method B (Two load tests) tests) ..................................................................................... 24

4.4.3

Verification method method ................................................................................................ 24

4.5

RESULTS: RESULTS: ....................................................................................................................... 25

4.6


4.7


REFERRENCES..................................................................................................................... REFERRENCES..................................................................................................................... 28

SEMESTER 2011/2012-1

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1. LAB 1: Ohm’s Law

1.1 AIM:

To verify Ohm’s Law.

1.2 APPARATUS:

The apparatus needed for this lab are: 

Variable voltage DC supply



Digital multimeter



Three resistors, 12 kΩ, 100 kΩ, and 20 kΩ

1.3 CIRCUIT DIAGRAM:

Ammeter

Voltmeter

Figure 1: Circuit diagram for Ohm’s Law experiment


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1.4 METHODOLOGY:

The lab was done following the procedures instructed carefully. First, the value of each resistors were measured using the digital multimeters and the measured values were recorded. Then, the circuit was constructed as shown in Figure 1 above. The power supply was adjusted to get a voltage of 2 V. After the setup process, the current flowing through each resistor was read and recorded in Table 1 as can be seen in result and discussion part below. The values of the currents were used to get the value of the calculated resistors using the formula: Resistors (Ω) =

   

Finally, the percentage error between the resistance calculated and resistance measured were achieved using the formula: Error (%) =


 

x 100

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1.5 RESULTS:

Table 1: Data tabulation for results of the experiment

Resistor (Ω)

Voltage (V)

Current (A)

listed

12 k

100 k

20 k

Resistance (Ω)

Resistance (Ω)

Calculated

Measured

% error

2.0

0.18 m

11.11 k

12 k

8.01 %

4.0

0.24 m

11.76 k

12 k

2.04 %

6.0

0.52 m

11.54 k

12 k

3.99 %

8.0

0.68 m

11.76 k

12k

2.04 %

10.0

0.82 m

12.19 k

12 k

1.56 %

2.0

0.02 m

100.0 k

100 k

0%

4.0

0.04 m

100.0 k

100 k

0%

6.0

0.06 m

100.0 k

100 k

0%

8.0

0.08 m

100.0 k

100 k

0%

10.0

0.1 m

100.0 k

100 k

0%

2.0

0.1 m

20.0 k

20 k

0%

4.0

0.2 m

20.0 k

20 k

0%

6.0

0.32 m

18.75 k

20 k

6.67 %

8.0

0.42 m

19.05 k

20 k

4.99 %

10.0

0.52 m

19.23 k

20 k

4.00 %


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1.6 DISCUSSION: a) Has Ohm’s Law been verified?

Yes. b) State the facts supporting your decision.

After the lab was done, it can be seen that the Ohm’s Law which is V = IR has been successfully verified. This is because the resistance values can be achieved using the current measured and the voltage supply. So, basically this fulfills the requirements of an Ohm’s Law which stated that voltage is equal to current times the resistance. This can also be seen in the graph plotted as attached at the end of this report. The graph shows that current is proportional to the voltage. So the higher the voltage is, the higher he current will be. c) State the probable factors which contributed to the discrepancies in the results.

First of all, a security measures during conducting this lab needed to be acknowledged and practiced. When measuring the resistors value, the best and safest way to do it is by plugging it into the bread board then only read the resistance value using the multimeter, not by holding the resistor with bare hand. By doing this, the measured valued of the resistors will be accurate as nearly as 100% with the listed value. Then, before connecting a supply voltage to the circuit, the circuit need be checked first by the supervisor in charge. This is to prevent short circuit inside the lab. But sometimes the error in reading the values of the resistors happened because of some technical problems such as multimeter failure or power supply that is over or under the desired voltage. All of the factors that have been discussed above contribute to the discrepancies in the results.


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Voltage Vs Current (12 k Ω)

Voltage (V) 12 10 8

Y-Values

6

Linear (Y-Values)

4

Current (mA)

2 0 0.18

0.24

0.52

0.68

0.82

Figure 2: Graph for voltage vs. current f or resistor 12 kΩ

Voltage (V)

Voltage Vs Current (100 k Ω)

12 10 8 Y-Values

6

Linear (Y-Values) 4 2

Current (mA)

0 0.02

0.04

0.06

0.08

0.1

Figure 3: Graph for voltage vs. current for resistor 100 k Ω


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Voltage Vs Current (20 kΩ)

Voltage (V) 12 10 8

Y-Values

6

Linear (Y-Values) 4 2

Current (mA)

0 0.1

0.2

0.32

0.42

0.52

Figure 4: Graph for voltage vs. current f or resistor 20 kΩ

1.7 CONCLUSION:

As for the conclusion, it can be seen that the main purpose of having this lab is a complete success. The Ohm’s Law has been successfully verified. This can be seen from the result itself. A resistance of a circuit can be calculated using the Ohm’s Law if the value of the supply voltage and the current are there. The discrepancies between the measured resistance and the calculated resistance maybe occurred because of some circumstances such as human error in reading the value of the current. This is because the current values were read by using an analog meter, so the reading won’t be 100 % accurate compared to reading by a digital multimeter. The discrepancies may also occur because of some technical error such as unstable power suppl y or a failure multimeter.


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2. LAB 2: Voltage Division

2.1 AIM:

The aims of having this lab are: 

To verify that the total resistance of a series circuit equals the sum of individual resistances



To verify the voltage divider rule. This rule states that the output voltage from a voltage divider is equal to the input voltage multiplied by the ratio of the resistance between the output terminals to the total resistance, which is:

VX = VS

 

2.2 APPARATUS:





Digital multimeter



Four resistors, 1 kΩ, 2 kΩ, 3 kΩ, and 1.5 kΩ


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Figure 5: Circuit diagram for resistance in series without power supply

Figure 6: Circuit diagram for resistance in series with power supply


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2.4 METHODOLOGY:

First of all, theories mention that when several resistors are used, the output is generally taken with respect to the ground as for example in Figure 7 below:

VX

Figure 7: Example circuit diagram for multiple resistances in series

In Figure 7 above, the value of output voltage VX can be calculated by using formula:

VX = VS VX = VS


   

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After understanding of this concept, the experiment was started. Each resistor was measured using the digital multimeter and these data were recorded as shown in Table 2 below. Then, the total resistance for a series connection was computed by adding the measured values and again the data were recorded in Table 2 below. By referring to the circuit in Figure 5, the connection was constructed. With the power off, the total resistance of the series connection was measured and the result was verified with the computed value. The voltage divider rule was then applied to each resistor one at a time to calculate the voltage across each of them. The measured values of resistances and a source voltage of 10V were used in this calculation. These data were again recorded in Table 2. Finally, the power supply of 10V was turned on and the voltage across each resistor was measured using the voltage meter. These results were added along with previous results in Table 2.

2.5 RESULTS:

Table 2: Data tabulation for the results of the e xperiment

Resistor

Listed Value

Measured Value

VX = VS (RX / RT)

VX (measured)

R 1

1 kΩ

0.99 kΩ

1.32 V

1.36 V

R 2

2 kΩ

1.95 kΩ

2.6 V

2.66 V

R 3

3 kΩ

2.93 kΩ

3.91 V

4.03 V

R 4

1.5 kΩ

1.42 kΩ

1.89 V

1.97 V

R T

7.5 kΩ

7.29 kΩ

9.72 V

10.02 V


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2.6 DISCUSSION: a) Has the two points of the aim been achieved?

Yes. b) State the facts supporting your decision for each point of the aim.

For the first aim which is to verify that the total resistance of a series circuit equals the sum of the individual resistances, it can be seen the aim has been proved to be correct as the results in Table 2 row number 5. If we add up the resistances that are connected in series, the sum will be equal with the total value of each individual resistance. The second aim which is to verify the voltage divider rule also has been proved to be correct. This can be seen in the result of the experiment in Table 2 column number 4. When compared to the measured values of the voltage across each resistor, the percentage error is small; hence it shows that the voltage divider rule has been applied correctly during the calculation. This also proves that the output voltage from a voltage divider is equal to the input voltage multiplied by the ratio of the resistance between the output terminals to the total resistance c) State the probable factors which contributed to the discrepancies in the results.

As can be seen in the result tabulation data in Table 2 above, the value of the voltage measured and the value of the voltage calculated using the voltage divider rule is a little bit different. These discrepancies in the results may occur because of some circumstances such as ignoring the safety measures or some technical errors from the apparatus used. A security measures during conducting this lab need to be acknowledged and practiced. When measuring the resistors value, the best and safest way to do it is by plugging it into the bread board then only read the resistance value using the


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multimeter, not by holding the resistor with bare hand. By doing this, the measured valued of the resistors will be accurate as nearly a s 100% with the listed value. Then, before connecting a supply voltage to the circuit, the circuit need be checked first by the supervisor in charge. This is to prevent short circuit inside the lab. But sometimes the error in reading the values of the resistors happened because of some technical problems such as multimeter failure or power supply that is over or under the desired voltage. All of the factors that have been discussed above contribute to the discrepancies in the results.

2.7 CONCLUSION:

As for the conclusion, it can be seen that the main purpose of having this lab is a complete success. The Ohm’s Law has been successfully verified. This can be seen from the result itself. A resistance of a circuit can be calculated using the Ohm’s Law if the value of the supply voltage and the current are there. The discrepancies between the measured resistance and the calculated resistance maybe occurred because of some circumstances such as human error in reading the value of the voltage. This is because the voltage values were read by using an analog meter, so the reading won’t be 100 % accurate compared to reading by a digital multimeter. The discrepancies may also occur because of some technical error such as unstable power suppl y or a failure multimeter.


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3. LAB 3: Superposition Theorem

3.1 AIM:


To verify that the superposition theorem

In any linear network containing several independent sources, the voltage across (or the current through) any element is the sum of the individual voltages (or sources) produced by each source acting alone. When determining the voltage (or current) due to an independent source, any remaining voltage sources are replaced by short circuits, and any remaining current sources are replaced by open circuits. The total current through any element is equal to the algebraic sum of the currents produced independently by each source. For a two-source network, if the current produced by one source is in the direction opposite to that produced by the other source, the resulting current is the difference of the two and has the direction of the larger. If the individual currents are in the same direction, the resulting current is the sum of the two and in the direction of either current. This rule holds for the voltages across any element as determined by the voltage polarities.

3.2 APPARATUS:





Digital multimeter



Three resistors, 4.7 kΩ, 6.8 kΩ, and 10 kΩ


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A

+

-

-

+

C

+

-

B

D

Figure 8: (a)

A

+

-

+

-

C

+ Jumper

-

B

D

Figure 9: (b)

A

-

+

-

+

C

+ Jumper

D

B

Figure 10: (c)


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3.4 METHODOLOGY:

First of all, the resistance value of each resistor was measured and recorded in Table 3 as can be seen below. Then, as per circuit diagram in Figure 8, the connection was constructed. After that, the 10 V source was removed and a jumper was placed between point C and D as shown in Figure 9. The total resistance seen by the 5 V source was computed, then the 5 V source was removed and then the resistance between point A and B was measured to confirm the calculation. These values of measured and computed resistances were recorded in Table 4. Then, the total current, IT, supplied by the 5 V source was computed. This current through R 1 was recorded as I1 in Table 4. Using the value of current I1, voltage divider rule was applied to determine the current that flows through R 2 and R 3. This calculation was made using the formula: I2 = IT (



)



and

I3 = IT (



)



After that, using the currents computed from above and the measured resistances

values, the expected voltage across each resistor of Figure 9 was

calculated. Then, the 5 V supply voltage was connected and the actual voltages present in the circuit was measured. These values were again recorded in Table 4. Then, the 5 V voltage supply was removed from the circuit and point A to B was connected by a jumper. The total resistance between point C and D was then computed. Again, the resistance between point C and D was measured to confirm the calculation. These values of resistances were also recorded in Table 4. Figure 10 was the constructed and the current through each resistor was

computed. Total current that flows through R 2 were divided between R 1 and R 3. The direction of the currents were also noted and recorded in Table 4. Again, using the values of the current computed above and the measured resistances, the voltage drop value across each resistor was computed. Then, the 10 V supply voltage was connected as shown in Figure 9 and the voltages across each


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resistor was measured. These values of voltage also were recorded in Table 4. Soon after that, the algebraic sum of the currents and voltages recorded in Table 4 was computed. Finally, the jumper between point A and B was removed and replaced by a 5 V supply voltage as shown in Figure 8. The voltage across each resistor was measure and the values of the voltage should agree with the algebraic sums.

3.5 RESULTS: Table 3: Tabulated data for value of resistors

Listed Value

Measured Value

R 1

4.7 kΩ

4.62 kΩ

R 2

6.8 kΩ

6.74 kΩ

R 3

10.0 kΩ

9.31 kΩ

Table 4: Tabulated data from result of experiment

Computed

Measured

Resistance

Resistance

8.74 kΩ

Computed

Computed

Measured

Current (A)

Voltage (V)

Voltage (V)

I1

I2

I3

V1

V2

V3

V1

V2

V3

2.63

2.29

2.14

2.72

2.29

2.29

3.14

6.74

2.98

3.16

6.85

3.16

0.51 4.45

5.12

0.44 4.56

5.45

0.44 4.55

5.45

8.59 kΩ 0.57 0.34 0.23

9.997 kΩ

9.830 kΩ 0.68

Total  Step 10 


1

0.32

0.11 0.66 0.55

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3.6 DISCUSSION: a) Has the superposition theorem been verified?

Yes.

b) State the facts supporting your decision for each point of the aim

In any linear network containing several independent sources, the voltage across (or the current through) any element is the sum of the individual voltages (or sources) produced by each source acting alone. This can be proven by the result of this experiment. It can be seen that the result shows that the voltage and current across each element is the sum of the individual voltage and current source.

c) State the probable factors which contributed to the discrepancies in the results.

As can be seen in the result tabulation data in Table 3 above, the value of the resistance listed and the value of the resistance measured using the multimeter is a little bit different. These differences ma y occur because of the multimeter itself. The multimeter will show more accurate values compared to the listed values announced by the factory that produced the resistors. As for the results in Table 4, it can be seen that the computed values of voltages and the measured values for the voltages also are a little bit different. These discrepancies in the voltage readings may occur because of some circumstances such as ignoring the safety measures or some technical errors from the apparatus used. A security measures during conducting this lab need to be acknowledged and practiced. When measuring the resistors value, the best and safest way to do it is by plugging it into the bread board then only read the resistance value using the


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multimeter, not by holding the resistor with bare hand. By doing this, the measured valued of the resistors will be accurate as nearly a s 100% with the listed value. Then, before connecting a supply voltage to the circuit, the circuit need be checked first by the supervisor in charge. This is to prevent short circuit inside the lab. But sometimes the error in reading the values of the resistors happened because of some technical problems such as multimeter failure or power supply that is over or under the desired voltage. All of the factors that have been discussed above contribute to the discrepancies in the results.

d) Prove that Kirchhoff’s voltage law is v alid for the circuit of Figure 8 using the algebraic sums from Table 4.

+

-

-

+

+

-

Figure 11: Figure 8 with the polarities according to the voltage supply

From the results gained by the experiment, it can be seen that the Kirchhoff’s voltage law have been proved. This is because the calculation of the voltage across each resistor using the algebraic sums agrees with the measurement values.


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d) Prove that Kirchhoff’s current law is valid for the circuit of Figure 8 using the algebraic sums from Table 4.

+

-

-

+

+ -

Figure 12: Figure 8 with the polarities according to the voltage supply

From the results gained by the experiment, it can be seen that the Kirchhoff’s current law have been proved. This is because the calculation of the current across each resistor using the algebraic sums agrees with the measurement values.

3.7 CONCLUSION:

As for the conclusion, it can be seen that the main purpose of having this lab is a complete success. The superposition theorem has been successfully verified. This can be seen from the result itself. The voltage across (or the current through) any element is the sum of the individual voltages (or sources) produced by each source acting alone. The discrepancies between the measured voltage and current and the calculated voltage and current maybe occurred because of some circumstances such as human error in reading the values. This is because the voltage and current values were read by using an analog meter, so the reading won’t be 100 % accurate compared to reading by a digital multimeter. The discrepancies may also occur because of some technical error such as unstable power suppl y or a failure multimeter.


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4. LAB 4: Thevenin’s Equivalent Circuit

4.1 AIM:


To determine, by two methods, the Thevenin’s equivalent circuit of a linear network containing several resistors



To verify the validity of the equivalent circuit so obtained

4.2 APPARATUS:


A 12 V dc supply



Digital multimeter



Six resistors, R 1 = 2.7 kΩ, R 2 = 5.6 kΩ, R 3 = 6.8 kΩ, R L1 = 1.8 kΩ, R L2 = 4.7 kΩ, and R L3 = 8.2 kΩ


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a

Ammeter

Voltmeter b Figure 13

4.4 METHODOLOGY:

4.4.1

Method A (Open circuit test and a load test)

First of all, the value of the load resistors R L1, R L2, and R L3 were measured and recorded in Table 5. Then as shown in Figure 13, the connection was made. The supply voltage was adjusted to 12 V and this value was maintained along the experiment. Then, the open circuit voltage at terminal a and b was measured. This open circuit voltage is also known as the Thevenin’s voltage, Veq of the equivalent voltage source. The value was recorded into Table 6. Then, load resistance R L1 was connected to terminals a and b. The

potential difference between terminal a and b with the load resistance connected was measured and the value was recorded. Finally, the Thevenin’s resistance of the equivalent source was calculated using formula: R eq = (R L1) (E – V) / V


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Method B (Two load tests)

First of all, the circuit as shown in Figure 13 was connected. Then, the load resistance, R L1 was connected to terminal a and b. The supply voltage was adjusted to 12 V and maintained along the experiment. Then, the open circuit voltage at terminal a and b was measured and the value was recorded in Table 7. Soon after that, the resistor R L1 was replaced with resistor R L2. Then, the

potential difference between terminals a and b was measured and the value was recorded. The Thevenin’s resistance was then calculated using formula: R eq = R L1R L2 (V2 – V1) / (V1R L2 – V2R L1) While the Thevenin’s voltage of the equivalent source was calculated using formula: Veq = V1 (R eq + R L1) / R L1 After calculating values above, the average values of Thevenin’s resistance and Thevenin’s voltage were calculated. The Thevenin’s equivalent circuit was drawn and the values of the parameters were indicated. 4.4.3

Verification method

To verify the methods above, firstly an ammeter and load resistor R L3 were connected to terminal a and b of the source. After adjusting the voltage supply to 12 V, the current flowing in the load resistor and the voltage drop through it were measured and recorded in Table 8. Then, based on the Thevenin’s equivalent circuit of the source, the current flowing in the load resistor and the voltage drop across it were calculated and recorded as well in Table 8.


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4.5 RESULTS: Table 5: Tabulated data for value of load resistors

Resistor

R L1

R L2

R L3

Listed Value

1.8 kΩ

4.7 kΩ

8.2 kΩ

Measured Value

1.78 kΩ

4.65 kΩ

8.17 kΩ

Table 6: Tabulated data for open circuit and load test

Supply

Open circuit

Terminal

Thevenin’s

Thevenin’s

Voltage (V)

voltage (V)

voltage (V)

voltage (V)

resistance

12

8.56

1.67

8.92

7.53

Table 7: Tabulated data for two load test

Supply

Terminal

Terminal

Thevenin’s

Thevenin’s

Voltage (V)

Voltage Load

Voltage Load

voltage (V)

resistance

R L1 (V)

R L2 (V)

1.67

3.32

8.57

7.49

12

Table 8: Load voltage and current

By measurement

By calculation

Load current (A)

Load Voltage (V)

Load current (A)

Load Voltage (V)

5.45

4.49

0.54

4.65


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4.6 DISCUSSION:

a) Make a comparison of the parameters of the Thevenin’s equivalent circuit obtained by the two methods using the relevant test results. What conclusions can you draw about the two circuits?

The two circuits gained using the two tests were implying that the theory is valid and can be proven. As can be seen, both tests produced almost consistent results toward each other.

b) Do the results of the verification test indicate that the Thevenin’s equivalent circuit obtained by each method is valid? Substantiate your answer by reference to the results.

As can be seen from the above results, the verification method indicates that both two tests using the two methods are valid.

c) State the factors that are most likely to have caused the differences in values of the parameters of the equivalent circuits obtained by the two methods?

The discrepancies between the measured voltage and current and the calculated voltage and current maybe occurred because of some circumstances such as human error in reading the values. This is because the voltage and current values were read by using an analog meter, so the reading won’t be 100 % accurate compared to reading by a digital multimeter. The discrepancies may also occur because of some technical error such as unstable power supply or a failure multimeter.


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d) State the adv antage that the Thevenin’s theorem offer for computing the load voltage across each of the load resistors tested in this experiment.

The advantage in performing the Thevenin conversion to the simpler circuit in this experiment is that it makes load voltage and load current so much easier to solve than in the original network. In real life, the advantage of using Thevenin’s theorem is that it can quickly determine which part of a circuit that goes wrong and need replacement without having to go through a lot of analysis again.

e) Figure 14 below shows a linear circuit and its Thevenin’s equivalent circuit. Explain why R 1 has no effect on the Thevenin circuit.

Figure 14

As can be noticed, R 1 is not taken into consideration, because the calculations were done in an open circuit condition between a and b, therefore no current flows through this part, which means there is no current through R 1 and therefore no voltage drop along this part.


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UEL ID: U1060761

4.7 CONCLUSION:

As for the conclusion, it can be seen that the main purpose of having this lab is a complete success. The Thevenin’s equivalent circuit of a linear network containing several resistors has been successfully determined. This can be seen from the result itself. The first method which is an open circuit test and load test has produced the Thevenin’s voltage and resistance of the circuit. The second method which is a two load test also has been successfully produced the Thvenin’s voltage and resistance. These two methods produced the same result consistent to each other. The discrepancies between the measured voltage and current and the calculated voltage and current maybe occurred because of some circumstances such as human error in reading the values. This is because the voltage and current values were read by using an analog meter, so the reading won’t be 100 % accurate compared to reading by a digital multimeter. The discrepancies may also occur because of some technical error such as unstable power supply or a failure multimeter.

5. REFERRENCES

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Dorf, Richard C. & Svoboda, James A. (2006) Introduction to Electric Circuits, John Wiley

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Irwin, David J.(1993) Basic Engineering Circuit Analysis, Macmillan Publishing Company

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Boylestad, Robert L.(2003) Introductory Circuit Analysis, Prentice Hall

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Hayt, W. H., Kemmerly, J. E. & Durbin, S. M.(2007) Engineering Circuit Analysis, McGraw Hill.



Nilsson, J. W. & Riedel, S. A.(2001) Electric Circuits, Prentice Hall


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Lab Report for circuit theory

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