Exercise 2: Kirchhoff s Current Law/2 Sources

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1 Exercise 2: Kirchhoff s Current Law/2 Sources EXERCISE OBJECTIVE When you have completed this exercise, you will be able to apply Kirchhoff s current law to a circuit having two voltage sources. You will verify your results by using measured data. DISCUSSION This circuit has two voltage sources connected with opposing polarities. through R3 is as shown. Three node currents (I R1, I R2, and I R3 ) are shown. I R1 = I R2 + I R3 124 Festo Didactic P0

2 Each of these currents can be represented by its voltage/resistance relationship. Which equation is correct? a. I R1 = V R1 /R1 b. I R2 = V R2 /R2 c. I R3 = V R3 /R3 d. All of the above In the equations are three unknowns: V R1, V R2, and V R3. However, according to Kirchhoff s voltage law, V R1 and V R2 voltage sources. Festo Didactic P0 125

3 LOOP 1: V R1 = V S1 V R3 LOOP 2: V R2 = V S2 + V R3 These equations are substituted into the current formula to allow for the circuit solution. 126 Festo Didactic P0

4 With what Kirchhoff s law(s) can you check your solutions? a. The sum of the voltages in any circuit loop equals zero. b. The current into any circuit node equals the current out of the same node. c. Both of the above If your solution indicates a negative current, your assumed current direction was incorrect. sign. PROCEDURE Locate the KIRCHHOFF SOLUTION WITH 2 SOURCES circuit block, and connect the circuit shown. Adjust V S1 to 10 Vdc. Festo Didactic P0 127

V S2 = Vdc (Recall Value 2) Based on the assumed current direction given in this

5 Measure V S1. V S1 = Vdc (Recall Value 1) Adjust V S2 to 10 Vdc. Measure V S2. NOTE: Enter the value of V S2, disregarding polarity. V S2 = Vdc (Recall Value 2) Based on the assumed current direction given in this circuit, what is the current formula for NODE 1? a. I R1 = I R3 + I R2 b. I R3 = I R1 + I R2 c. I R3 = I R1 I R2 128 Festo Didactic P0

In this circuit, the voltage drop across which resistor allows for a complete circuit solution? a. R1 b. R2 c. R3 With respect to circuit common, measure the voltage across R3.

6 In this circuit, the voltage drop across which resistor allows for a complete circuit solution? a. R1 b. R2 c. R3 With respect to circuit common, measure the voltage across R3. V R3 = Vdc (Recall Value 3) Based on your measurement, is the voltage at NODE 1 positive or negative with respect to circuit common? a. positive b. negative Based on your measurement and polarity of V R3 a. no b. yes Festo Didactic P0 129

7 Calculate the current through R3. I R3 = V R3 /R3 V R3 = Vdc (Step 5, Recall Value 3) I R3 = ma (Recall Value 4) Determine the current through R1. I R1 = (V S1 V R3 )/R1 V R3 = Vdc (Step 5, Recall Value 3) V S1 = Vdc (Step 2, Recall Value 1) I R1 = ma (Recall Value 5) Use Ohm s law to calculate V R1. I R1 = ma (Step 9, Recall Value 5) V R1 = Vdc (Recall Value 6) 130 Festo Didactic P0

8 Determine the current through R2. I R2 = (V S2 + V R3 )/R2 V R3 = Vdc (Step 5, Recall Value 3) V S2 = Vdc (Step 2, Recall Value 2) I R2 = ma (Recall Value 7) Use Ohm s law to calculate V R2. V R2 = I R2 x R2 I R2 = ma (Step 11, Recall Value 7) V R2 = Vdc (Recall Value 8) I R1 = I R2 + I R3 I R1 = ma (Step 9, Recall Value 5) I R2 = ma (Step 11, Recall Value 7) I R3 = ma (Step 8, Recall Value 4) Do the NODE 1 currents agree with Kirchhoff s current law? a. no b. yes Festo Didactic P0 131

9 V S1 = Vdc (Step 2, Recall Value 1) V S2 = Vdc (Step 2, Recall Value 2) V R1 = ma (Step 10, Recall Value 6) V R2 = ma (Step 12, Recall Value 8) V R3 = ma (Step 5, Recall Value 3) Do the voltages agree with Kirchhoff s voltage law for each loop? a. no b. yes CONCLUSION You should apply Kirchhoff s current law to determine a circuit solution. The current into a circuit node equals the current out of the same circuit node. After you know the voltage of the element that is common to both loops, apply Ohm s law to determine each circuit current. An incorrect assumed current direction is indicated by a negative sign. 132 Festo Didactic P0

10 REVIEW QUESTIONS 1. Locate the KIRCHHOFF SOLUTION WITH 2 SOURCES circuit block, and connect the circuit shown. Adjust each voltage source to 10 Vdc ±5% Place CM switch 18 in the ON position to change the value of R2. What is the equation for I 3 with current direction as indicated? a. I 3 = I 1 + I 2 b. I 3 = I 1 I 2 c. I 3 = I 2 I 1 d. I 3 + I 1 + I 1 = 0 Festo Didactic P0 133

11 2. With respect to circuit common, the voltage across R3 a. cannot be measured. b. is about 4.69 V. c. is about V. d. is about V. 3. Based on this circuit, what is the value of V R2? a. V S1 V R1 b. V S2 + V R3 c. V R3 + V R1 d. None of the above 4. With CM 18 active, about what is the value of R2? a. cannot be determined b c d What is the value of I 3? a. cannot be determined b ma c ma d ma Note: Make sure all CMs are cleared (turned off) before proceeding to the next section. 134 Festo Didactic P0

Exercise 2: Millman s Theorem

Exercise 2: Millman s Theorem EXERCISE OBJECTIVE When you have completed this exercise, you will be able to solve a circuit by applying Millman s theorem. You will verify your results by comparing calculated