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Name: ______________________________
ECET 231 - Circuit Analysis I
Lab 7
Mesh Analysis and Superposition
Objective:
Students successfully completing this preparatory exercise will accomplish the
following objectives:
1. Gain increased understanding of the applications of mesh analysis.
2. Verify, by measurements, the results of mesh anaylsis.
3. Demonstrate, by measurements, the theorem of superposition as a means to
achieve results similar to those of objective 2.
Equipment:
Power supplies (2), Digital Multimeter (DMM), breadboards (2), resistors (3.3 kΩ,
1 kΩ, 560 Ω), jumper wires.
Procedure:
1.
For the circuit below, use mesh analysis to determine the current in each branch (I1, I2, I3)
by following the steps below.
a
R1 = 3.3 k
E1
10 V
b
R2 = 1 k
R3
560
c
E2
5V
Figure 1: Series-parellel circuit with two voltage sources
Assume that the left mesh has a loop current I1 and the right mesh has a loop current I2.
Write the KVL equation for the left mesh.
Write the KVL equation for the right mesh.
Using determinants, solve for I1 (show the ratio of matrices used – solve by calculator).
Record your results in Table 1 below.
Using determinants, solve for I2 (show the ratio of matrices used – solve by calculator).
Record your results in Table 1 below.
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Given that the resistor current I3 equals the difference in the loop currents calculated above,
find the value of I3 (show your calculation) Record your results in Table 1 below.
Table 1: Currents calculated by mesh analysis
Quantity
Calculated Value
I1
I2
I3
2.
Using the currents calculated in the previous step, find the resistor voltages VR1, VR2 and
VR3. Show your calculations in Table 2 below.
Table 2: Calculated node voltages
Quantity
Calculation
VR1
VR2
VR3
3.
Select three resistors, R1, R2, R3, of the values shown in Figure 1. Measure each resistor.
Record their measured values in Table 3 below.
Table 3: Measure resistor values
Resistor
Measured Value
R1
R2
R3
Tie the grounds of two power supplies together with a probe wire. Set one power supply,
E1, to 10 V. Set the second power supply, E2, to 5 V. Turn off both supplies and assemble
the circuit. Use a second breadboard as a connection point for E2 and use jumper wires to
bridge E2 to the circuit.
Have the instructor inspect your circuit before turning on the power supplies.
4.
Measure the current through each branch of the circuit (I1, I2, I3), and the resistor voltages
(VR1, VR2, VR3). Be sure to orient your probes so that currents and voltages will register a
positive value. Record your results in Table 4 below.
Table 4: Measured currents and voltages
Quantity
Measured Value
I1
I2
I3
VR1
VR2
VR3
5.
Disconnect source E2 from the circuit. Connect a jumper wire across the terminals to which
it was connected. Repeat the measurements of the previous step and record your results
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in Table 5 below. Orient your meter probes so that the positive and negative probes are
both on the corresponding nodes used for your previous measurements.
Table 5: Measured voltages and currents due to source E1 alone
Quantity
Measured Value
I1
I2
I3
VR1
VR2
VR3
6.
Remove the jumper wire placed in the previous step and reconnect source E2. Disconnect
source E1 from the circuit. Connect a jumper wire across the terminals to which it was
connected. Repeat the measurements of the previous step and record your results in
Table 6 below. Orient your meter probes so that the positive and negative probes are both
on the corresponding nodes used for your previous measurements.
Table 6: Measured voltages and currents due to source E2 alone
Quantity
Measured Value
I1
I2
I3
VR1
VR2
VR3
7.
Using your measured data from the previous two steps, calculate the sums shown in Table
7 below. Also calculate the percent error of the summed values with respect to the
measured values of each quantity when both power supplies were operating
simultaneously (from Table 4).
Table 7: Summed voltages and currents due to individual power supplies
Quantity
Measured Value
% Error
(vs. Table 4 Data)
I1 (E1) + I1(E2)
I2 (E1) + I2(E2)
I3 (E1) + I3(E2)
VR1(E1) + VR1(E2
VR2(E1) + VR2(E2)
VR3 (E1) + VR3(E2)
Do your calculations compare favorably? ____________
State in words how these calculations support or fail to support the theorem of superposition.