lab report for circuit theory
TRANSCRIPT
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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
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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
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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
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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
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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 %
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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.
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Figure 2: Graph for voltage vs. current for resistor 12 k
Figure 3: Graph for voltage vs. current for resistor 100 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
Voltage Vs Current (100 k)
Y-Values
Linear (Y-Values)
Current (mA)
Voltage (V)
Voltage (V)
Current (mA)
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Figure 4: Graph for voltage vs. current for resistor 20 k
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
Voltage Vs Current (20 k)
Y-Values
Linear (Y-Values)
Current (mA)
Voltage (V)
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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
2.2APPARATUS:The apparatus needed for this lab are:
Variable voltage DC supply Digital multimeter Four resistors, 1 k, 2k, 3 k, and 1.5k
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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
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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
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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 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
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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
c) State the probable factors which contributed to the discrepancies in the
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
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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.
3.2APPARATUS:The apparatus needed for this lab are:
Variable voltage DC supply Digital multimeter Three resistors, 4.7 k, 6.8 k, and 10k
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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
++
+
--
-
-
-
-+ +
+
++
+
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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
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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 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
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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.
c) State the probable factors which contributed to the discrepancies in the
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
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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.
+
+ +
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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
4.2APPARATUS:The apparatus needed for this lab are:
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
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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
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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.
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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.
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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