Lab Report for circuit theory

8/13/2019 Lab Report for circuit theory

1/28

EE 1002

CIRCUIT THEORY

LAB REPORT

Contents

1. LAB 1: Ohms Law ................................................................................................................... 3

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


2/28

EE1002 [Lab report] UEL ID: U1060761

SEMESTER 2011/2012-1 Page | 2

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

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

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

3.3 CIRCUIT DIAGRAM:................................................................................................... 16

3.4 METHODOLOGY: ........................................................................................................ 17

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

3.6 DISCUSSION:................................................................................................................. 19

3.7 CONCLUSION: .............................................................................................................. 21

4. LAB 4: Thevenins Equivalent Circuit ................................................................................. 22

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

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

4.3 CIRCUIT DIAGRAM:................................................................................................... 23

4.4 METHODOLOGY: ........................................................................................................ 23

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

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

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

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

4.6 DISCUSSION:................................................................................................................. 26

4.7 CONCLUSION: .............................................................................................................. 28

5. REFERRENCES..................................................................................................................... 28


3/28



1. LAB 1: Ohms Law1.1AIM:To verify Ohms Law.

1.2APPARATUS:The apparatus needed for this lab are:

Variable voltage DC supply Digital multimeter Three resistors, 12 k, 100 k, and 20 k

1.3CIRCUIT DIAGRAM:

Figure 1: Circuit diagram for Ohms Law experiment

Ammeter

Voltmeter


4/28



1.4METHODOLOGY: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 () =

Finally, the percentage error between the resistance calculated and resistance

measured were achieved using the formula:

Error (%) =

x 100


5/28



1.5RESULTS:

Table 1: Data tabulation for results of the experiment

Resistor ()

listed

Voltage (V) Current (A) Resistance ()

Calculated

Resistance ()

Measured

% error

12 k

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 %

100 k

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 %

20 k

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 %


6/28



1.6DISCUSSION:a) Has Ohms Law been verified?

Yes.

b) State the facts supporting your decision.

After the lab was done, it can be seen that the Ohms 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 Ohms 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.


7/28



Figure 2: Graph for voltage vs. current for resistor 12 k


0

2

4

6

8

10

12

0.18 0.24 0.52 0.68 0.82

Voltage Vs Current (12 k)

Y-Values

Linear (Y-Values)

0

2

4

6

8

10

12

0.02 0.04 0.06 0.08 0.1


Y-Values

Linear (Y-Values)

Current (mA)

Voltage (V)

Voltage (V)

Current (mA)


8/28




1.7CONCLUSION:As for the conclusion, it can be seen that the main purpose of having this lab is

a complete success. The Ohms Law has been successfully verified. This can be

seen from the result itself. A resistance of a circuit can be calculated using the

Ohms 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 wont 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.

0

2

4

6

8

10

12

0.1 0.2 0.32 0.42 0.52


Y-Values

Linear (Y-Values)

Current (mA)

Voltage (V)


9/28



2. LAB 2: Voltage Division

2.1AIM:

The aims of having this lab are:

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

To verify the voltage divider rule. This rule states that the output voltagefrom 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


Variable voltage DC supply Digital multimeter Four resistors, 1 k, 2k, 3 k, and 1.5k


10/28



2.3CIRCUIT DIAGRAM:

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

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


11/28



2.4METHODOLOGY: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 7below:

Figure 7: Example circuit diagram for multiple resistances in series

In Figure 7above, the value of output voltage VXcan be calculated by usingformula:

VX= VS

VX= VS

VX


12/28



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 2below. Then, the total resistance for a series connection was computed

by adding the measured values and again the data were recorded in Table 2below.

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.

2.5RESULTS:

Table 2: Data tabulation for the results of the experiment

Resistor Listed Value Measured Value VX = VS (RX / RT) VX (measured)

R1 1 k 0.99 k 1.32 V 1.36 V

R2 2 k 1.95 k 2.6 V 2.66 V

R3 3 k 2.93 k 3.91 V 4.03 V

R4 1.5 k 1.42 k 1.89 V 1.97 V

RT 7.5 k 7.29 k 9.72 V 10.02 V


13/28



2.6DISCUSSION: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 2row 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


results.

As can be seen in the result tabulation data in Table 2above, 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


14/28


15/28



3. LAB 3: Superposition Theorem

3.1AIM:The aims of having this lab are:

To verify that the superposition theoremIn 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.


Variable voltage DC supply Digital multimeter Three resistors, 4.7 k, 6.8 k, and 10k


16/28



3.3CIRCUIT DIAGRAM:

Figure 8: (a)

Figure 9: (b)

Figure 10: (c)

Jumper

Jumper

A

A

A

B

B

B

C

C

C

D

D

D

++

+

--

-

-

-

-+ +

+

++

+

--

-


17/28



3.4METHODOLOGY:First of all, the resistance value of each resistor was measured and recorded

in Table 3as 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 R1was recorded as I1in Table 4. Using the value of current I1,

voltage divider rule was applied to determine the current that flows through R2and

R3. 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 10was the constructed and the current through each resistor was

computed. Total current that flows through R2were divided between R1and R3. 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 9and the voltages across each


18/28



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 4was

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.

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

Listed Value Measured Value

R1 4.7 k 4.62 k

R2 6.8 k 6.74 k

R3 10.0 k 9.31 k

Table 4: Tabulated data from result of experiment

Computed

Resistance

Measured

Resistance

Computed

Current (A)

Computed

Voltage (V)

Measured

Voltage (V)

I1 I2 I3 V1 V2 V3 V1 V2 V3

8.74 k 8.59 k

0.57 0.34 0.23

2.63 2.29 2.14 2.72 2.29 2.29

9.997 k 9.830 k

0.68 1 0.32

3.14 6.74 2.98 3.16 6.85 3.16

Total 0.11 0.66 0.55 0.51 4.45 5.12 0.44 4.56 5.45

Step 10 0.44 4.55 5.45


19/28



3.6DISCUSSION: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.


results.

As can be seen in the result tabulation data in Table 3above, the value of

the resistance listed and the value of the resistance measured using the multimeter

is a little bit different. These differences may 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


20/28


21/28



d) Prove that Kirchhoffs 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

Kirchhoffs 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.

3.7CONCLUSION: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 wont 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.

+

+ +

-

--


22/28



4. LAB 4: Thevenins Equivalent Circuit4.1AIM:The aims of having this lab are:

To determine, by two methods, the Thevenins equivalent circuit of a linearnetwork containing several resistors

To verify the validity of the equivalent circuit so obtained


A 12 V dc supply Digital multimeter Six resistors, R1= 2.7 k, R2= 5.6 k,R3= 6.8 k, RL1= 1.8 k,

RL2= 4.7 k, and RL3= 8.2 k


23/28



4.3CIRCUIT DIAGRAM:

Figure 13

4.4METHODOLOGY:

4.4.1 Method A (Open circuit test and a load test)First of all, the value of the load resistors RL1, RL2, and RL3 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 Thevenins

voltage, Veq of the equivalent voltage source. The value was recorded into

Table 6. Then, load resistance RL1 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 Thevenins resistance of

the equivalent source was calculated using formula:

Req= (RL1) (EV) / V

Voltmeter

Ammeter

-

a

b


24/28


25/28


26/28



4.6DISCUSSION:

a) Make a comparison of the parameters of the Thevenins equivalent circuitobtained 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 Theveninsequivalent 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 invalues 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 wont 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.


27/28



d) State the advantage that the Thevenins theorem offer for computing theload 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 Thevenins

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 Thevenins equivalentcircuit. Explain why R1has no effect on the Thevenin circuit.

Figure 14

As can be noticed, R1is 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 R1and

therefore no voltage drop along this part.


28/28


4.7CONCLUSION:As for the conclusion, it can be seen that the main purpose of having this lab is a

complete success. The Thevenins 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

Thevenins voltage and resistance of the circuit. The second method which is a two

load test also has been successfully produced the Thvenins 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 wont 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

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

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

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

Documents

Lab Report for circuit theory