Capitol College

Spring Semester 2000

# Circuit Theory: EE - 159

Lab Experiment #4

## Network Theorems

Andy Buettner

Instructor: Dr. Thomas

Due: Friday, April 07 2000

Section Page #

1. Title Page???????????? 1

1. Objective????????????. 3

1. Equipment Used?????????.. 3

1. Equipment used?????????.. 3

2. Materials used??????????. 3

1. Procedures???????????... 3

1. Part 1?????????????... 3

2. Part 2?????????????... 4

1. Results?????????????. 4

1. Table 1:????????????... 4

2. Table 2:????????????... 4

3. Diagram 1:???????????.. 5

4. Table 3:????????????... 5

5. Diagram 2:???????????.. 5

1. Answers to Lab Questions?????. 6

1. Conclusions??????????... 10

1. Attachments??????????... 10

Objective

The objective of this lab is to study the interactions in more complex circuits in order to prove Thevenin's and Norton's theorems as well as the theorem of superposition. To do this, a circuit is constructed and measurements are made. The results are then compared to values that will be calculated.

Equipment Used

1. Equipment used:

1. ET - 3100 Trainer #1054, 1514

2. Fluke DMM #1321, 31101515

3. EE - 159 Lab kit

1. Parts used:

1. 220W Resistor

2. 330W Resistor

3. 470W Resistor

4. 1KW Resistor x2

5. 2.2KW Resistor

6. 3.3KW Resistor

Procedures

I) Part 1:

1. Analyze the circuit below to find the Thevenin's equivalent.

1. Measure the resistances of the individual resistors.

2. Assemble the circuit

3. Power the circuit to 10v

4. Measure the voltage across the gap.

5. Place the 1kW resistor across the gap and measure the voltage drop across it

6. Place a 470 W resistor across the gap and measure the voltage drop across it.

7. Turn the trainer off and short out the power supply.

8. Measure the total resistance of the circuit at the gaps.

II) Part 2:

1. Measure the resistors needed to construct the following circuit.

2. Construct the following circuit:

1. Power the trainer and set the voltages accordingly.

2. Measure the voltage drop across each resistor.

Results

Table 1: Resistor Values for part 1

Resistor #

1

2

3

### Expected Value

330W

220W

1kW

Actual Value

329.4W

218.6W

.982kW

Table 2: Voltage values for Rx

 Resistor # none 1 2 Listed resistance W 470W 1kW Actual resistance W 456W 1.003kW Voltage drop 3.989v 1.161v 1.895v

Diagram 1: Circuit for Part 1 (enlarged view)

Table 3: Results for Part 2

Resistor #

1

2

3

### Expected Value

1.2KW

2.2KW

3.3KW

Actual Value

1.210KW

2.171KW

3.247KW

Voltage Drop

5.77v

4.21v

9.20v

Diagram 2: Diagram for Part 2: (Enlarged view)

1) Q: What is the Thevenin's equivalent voltage for circuit 1 and how does it compare with the measured voltage?

A: 3.989v: This is an exact value.

Work:

2) Q: What is the Thevenin's equivalent resistance for circuit 1, and how does it compare to the value observed?

A: 1060.4W: With an error of 5.53%

Work:

3) Q: Explain Thevenin's theorem; do the results verify it?

A: Thevenin's theorem states that if there is a complex resistor, and source network that acts on a single resistor, the circuit can be reduced to a circuit containing only one resistor in series with one voltage source. The results verify this because they contain negligible between the values using the theorem and the values that were observed.

Work:

• Work shown in problems Q1 and Q2 !

4) Q: What was the voltage across the 470W resistor, and how does it compare with the calculated value?

A: The voltage was 1.161v: With an error of 5.20%

Work:

5) Q: What were the expected and measured resistances across the 1kW resistor?

A1: Observed: 1.895v

A2: Calculated: 1.884v

Work:

6) Q: Do these results uphold Thevenin's theorem?

A: Yes they do. The errors between the measured and the calculated are very small.

Work:

7) Q: What was the current through the 470W resistor?

A1: Calculated: 2.528ma

A2: Observed: 2.529ma

Work:

8) Q: Repeat of question 6

A: Repeat of question 6.

Work:

• No work is necessary for this problem. !

9) Q: What are the individual currents and voltages across the resistors for Circuit 2, and what is the error for the voltages?

A1: Observed: Vr1 = 5.77v Vr2 = 4.21v Vr3 = 9.20v

A2: Calculated: Vr1 =6.322v Vr2 = 6.148v Vr3 = 9.218v

A3: Calculated: Ir1 = 5.225ma Ir2 = 2.832ma Ir3 = 2.839ma

A4: % error: R1 = 8.73% R2 = 31.52% R3 = .195%

Work:

• Work shown on next page. !

10) Q: What effect does the internal resistance of the trainer have on the circuit?

A: The effect would is slightly lower observed currents, thus increasing the %error.

Work:

• No work is necessary for this problem. !

Conclusions

In conclusion, this lab help affirm that Thevenin's theorem and the theorem of superposition are useful in solving various types of circuits. This is shown by the small error between the calculated values used to solve the various parts of each of the two circuits and the observed results. Only one of the readings was off by a significant figure. I believe that inaccurate equipment as well little compensation for the properties of the trainer were the cause of the error. Finally, this lab proves that these theories can be successfully used to simplify and solve various circuits.

Attachments

#### A) Original handout

B) Copies of lab papers

C) Copies of calculations