ET310_Lab2_G00304033
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Lab 2: Circuit Analysis Techniques in Multisim
Grantham University
Date: February 23, 2024
Introduction:
This lab is intended to explore the application of circuit analysis techniques to a resistive circuit in Multisim. A mesh analysis using Kirchoff’s voltage law will be performed on the current loops within the circuit to determine currents and power delivery and dissipation. The first circuit analysis will incorporate a dependent current source equal to 5 times i1. In the second circuit, the dependent current
source will be removed. The results will be compared to observe any change in the power delivered and power dissipated. Equipment/Components:
Multisim
Power supply: 1V, 8V
Dependent current source: 5i1
Resistors: 4Ω, 3Ω, 1Ω, 2Ω
Agilent multimeter
Wattmeter
Procedure: The following screenshots show the Multisim circuits to be analyzed:
Calculations with dependent source (5i1):
Mesh 1:
−
1
+
4
i
1
+
3
(
i
1
−
i
2
)
+
1
(
i
1
−
i
3
)
=
0
8
i
1
−
3
i
2
−
i
3
=
1
Dependent source:
5
i
1
−
i
2
+
i
3
=
0
Super mesh:
1
(
i
3
−
i
1
)
+
3
(
i
2
−
i
1
)
−
8
+
2
i
3
=
0
−
4
i
1
+
3
i
2
+
3
i
3
=
8
After solving system of equations:
i
1
=
19
A
i
2
=
61.5
A
i
3
=−
33.5
A
Power supplied:
P
1
V
=
Vi
1
=
1
V
(
19
A
)
=
19
W
Calculations without dependent source (5i1):
Mesh 1:
−
1
+
4
i
1
+
3
(
i
1
−
i
2
)
+
1
(
i
1
−
i
2
)
=
0
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8
i
1
−
4
i
2
=
1
V
Mesh 2:
−
8
+
2
i
2
+
4
(
i
2
−
i
1
)
=
0
−
4
i
1
+
6
i
2
=
8
V
After solving system of equations:
i
1
=
1.1875
A
i
2
=
2.125
A
Power supplied:
P
1
V
=
Vi
1
=
1.1875
W
Results:
The following screenshot shows the measurement for current (i1):
The following screenshot show the measurement for power delivered by the 1V source:
The following screenshot shows the measurement for voltage drop across each resistor so that power dissipated by each resistor can be calculated:
The following screenshot shows the measurement for current (i1) without the dependent source:
The following screenshot show the measurement for power delivered by the 1V source:
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The following screenshot shows the measurement for voltage drop across each resistor so that power dissipated by each resistor can be calculated:
Calculated Current (i1)
Calculated Power supplied by 1V
Measured Current (i1)
Measured Power supplied by 1V
With Dependent Source (5i1)
19 A
19 W
18.999 A
19 W
Without Dependent Source (5i1)
1.1875 A
1.1875 W
1.187 A
1.188 W
Analysis:
With the dependent source in the circuit, the calculated and measured values for current (i1) differ by only .001 W. This difference can be attributed to the 5% tolerance on the resistors. The calculated and measured values for power delivered by the 1V source are the same. Without the dependent source in the circuit, the calculated and measured values for current (i1) differ by only .0005 W. This difference can be attributed to the 5% tolerance on the resistors. The calculated and measured values for power delivered by the 1V source also differ by .0005 W. This difference is also attributed to the 5% tolerance on the resistors.
Power delivered/dissipated with dependent source calculations:
P
delivered
=
1
V
(
i
1
)+
5
i
1
(
52.5
V
+
67
V
)
+
8
V
(
i
2
)
P
delivered
=
19
A
+
5
(
19
A
) (
52.5
V
+
67
V
)
+
8
(
61.5
A
)
=
11,863.5
W
P
dissipated
=
127.5
V
2
3
Ω
+
52.5
V
2
1
Ω
+
67
V
2
2
Ω
+
19
A
2
(
4
Ω
)
=
11,863.5
W
Power delivered is equal to power dissipated.
Power delivered/dissipated without dependent source calculations:
P
delivered
=
1
V
(
i
1
)
+
8
V
(
i
2
)
=
1
(
1.1875
A
)
+
8
V
(
2.125
A
)
=
18.1875
W
P
dissipated
=
4
Ω
(
1.187
A
2
)
+
2.813
V
2
3
Ω
+
0.9375
V
2
1
Ω
+
4.25
V
2
2
Ω
=
18.1836
W
Power delivered is equal to power dissipated, however a slight difference of 0.0039 W exists.
After removing the dependent power source from the circuit, the power supplied/delivered decreased dramatically. The dependent current source alters the current distribution and voltages in the circuit which is why a reduction in power delivery is observed. Conclusion/Discussion:
The results from the resistive circuit Multisim simulations demonstrate that the measured values correlate with the calculated values for current (i1) and power delivered by the 1V source. The small discrepancy in the measured value is attributed to the 5% resistor tolerance. It was also shown that power supplied is equal to the sum of power dissipated in each resistor for each of the circuits. When the dependent current source was removed, the total power delivered decreased significantly. References:
Nilsson, J. W., & Riedel, S. A. (2019). Electric circuits
. Pearson.
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