Kirchhoff’s Solution with 2 Sources
Exercise 1: Kirchhoff’s Voltage Law/2 Sources
EXERCISE OBJECTIVE
When you have completed this exercise, you will be able to apply Kirchhoff’s voltage law to a circuit
having two voltage sources. You will verify your results by using measured data.
DISCUSSION
This is a circuit with 2 voltage sources, VS1 and VS2, connected with opposing polarities.
Even though the circuit has 2 voltage sources, Kirchhoff’s law still applies to the circuit.
There are 3 loops in this circuit.
One loop, which we will call LOOP 1, includes VS1, R3, and R1.
Another loop, which we will call LOOP 2, includes VS2, R2, and R3.
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Kirchhoff’s Solution with 2 Sources
What is the third loop composed of?
a. VS1, R3, and R1
b. VS2, R3, and R2
c. VS1, R1, R2, and VS2
You can generate the loop equations by applying Kirchhoff’s voltage law to LOOP 1 and LOOP 2.
The LOOP 1 equation is VS1 – VR3 – VR1 = 0.
What is the LOOP 2 equation?
a. VS1 – VR3 – VR1 = 0
b. VS2 – VR2 + VR3 = 0
PROCEDURE
฀
Locate the KIRCHHOFF SOLUTION WITH 2 SOURCES circuit block, and connect the
circuit shown.
S1)
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to 10 Vdc.
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Kirchhoff’s Solution with 2 Sources
฀
Measure VS1.
VS1 =
Vdc (Recall Value 1)
Adjust the second variable source (VS2) to 10 Vdc.
฀
Measure VS2.
NOTE: Do not assign a + or – sign to your measurement.
VS2 =
฀
Vdc (Recall Value 2)
VS1, R1, and R3 form which loop in this circuit?
a. LOOP 1
b. LOOP 2
฀
VS2, R2, and R3 form which loop in this circuit?
a. LOOP 1
b. LOOP 2
฀
The third loop is composed of
a. LOOP 1 and LOOP 2.
b. VS1, R1, R2, and VS2.
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Kirchhoff’s Solution with 2 Sources
฀
Measure the voltage drop of R1.
NOTE: Do not assign a + or – sign to your measurement.
VR1 =
฀
Measure the voltage drop of R2.
VR2 =
฀
Vdc (Recall Value 4)
Measure the voltage drop of R3.
VR3 =
฀
Vdc(Recall Value 3)
Vdc (Recall Value 5)
Based on the loop relationships, the proper voltage polarities have been assigned to the
voltage drops in this circuit.
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Kirchhoff’s Solution with 2 Sources
฀
Using the values you measured and the signs shown in the circuit, calculate the voltage
distribution of LOOP 1.
VS1 – VR3 – VR1 = 0
฀
VS1 =
Vdc (Step 2, Recall Value 1)
VR1 =
Vdc (Step 7, Recall Value 3)
VR3 =
Vdc (Step 9, Recall Value 5)
VLOOP 1 =
Vdc (Recall Value 6)
Using the values you measured and the signs shown in the circuit, calculate the voltage
distribution of LOOP 2.
VS2 – VR2 + VR3 = 0
฀
VS2 =
Vdc (Step 3, Recall Value 2)
VR2 =
Vdc (Step 8, Recall Value 4)
VR3 =
Vdc (Step 9, Recall Value 5)
VLOOP 2 =
Vdc (Recall Value 7)
Do your calculations agree with Kirchhoff’s voltage law?
a. no
b. yes
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Kirchhoff’s Solution with 2 Sources
฀
Does Kirchhoff’s voltage law apply to a circuit with two voltage sources?
a. no
b. yes
CONCLUSION
•
The algebraic sum of the voltage source(s) and voltage drops in any loop must equal zero.
•
You must apply the polarities of each voltage drop with respect to Kirchhoff’s law.
REVIEW QUESTIONS
1. Locate the KIRCHHOFF SOLUTION WITH 2 SOURCES circuit block, and connect the circuit as
shown.
Adjust VS1 to 10 Vdc.
Adjust VS2 to –10 Vdc.
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Kirchhoff’s Solution with 2 Sources
How many loops are in this circuit?
a.
b.
c.
d.
4
3
2
1
2. Place CM switch 17 in the ON position to change the value of R1. Using the VS2, R2, and R3 circuit
loop, with VS2 = 10 V and VR2 = 15.22 Vdc, what is VR3?
a.
b.
c.
d.
+5.22 V
–5.22 V
Either of the above
None of the above
3. Measure the voltage drops of your circuit. With respect to circuit common, the voltage drop of R3
a.
b.
c.
d.
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does not depend on the circuit values.
is negative.
is positive.
cannot be determined.
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Kirchhoff’s Solution with 2 Sources
4.
SOURCES circuit block?
a.
b.
c.
d.
A
B
C
D
5. With respect to circuit common, the voltage drop of R3 in this circuit
a.
b.
c.
d.
is positive.
is negative.
depends on the resistor values.
cannot be determined.
Note: Make sure all CMs are cleared (turned off) before proceeding to the next section.
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