1. Principles & Applications Complex-Circuit Analysis
Electricity
Principles & Applications
Sixth Edition
Richard J. Fowler
Chapter 6
Complex-Circuit Analysis
© Glencoe/McGraw-Hill

2. INTRODUCTION Superpositon Theorem Voltage Sources Thevenin’s Theorem
Norton’s Theorem

3. Superposition Technique
110 V
10 W
30 W
20 W B2 B1
2 A
3 A
1 10 V
Rtyu
5 A
Replace B2
with a short
and calculate the currents.
110 V
20 W
10 W
30 W
110 V
Rtyu
4 A
1 A
3 A
Replace B1
with a short
and calculate the currents.
10 W
30 W
110 V
20 W
1 A
7 A
8 A
Algebraically add the two currents for each resistor.

4. Verification of Superposition Results Using Circuit Measurements
The dark bars on the ammeters are the negative terminals.
Notice that both the directions and magnitudes of the currents agree with those obtained by the superposition method.

5. Voltage Sources V V V V Ideal Source Equivalent-Circuit Source No load
Loaded V
15 V
Voltage does
not change
when loaded.
Equivalent-Circuit Source
No load
15 V V
Loaded V
13 V
Voltage changes
when loaded.

6. Thevenizing a Complex Circuit
10 W
20 W B2 B1
30 W R2 R2
30 W
VTH = 36.7 V
RTH = 6.7 W
Replace B1 and B2
Remove R2
and calculate VTH.
with shorts
and calculate RTH. e R2
30 W
RTH
6.7 W
VTH
36.7 V - +
Draw the Thevenin equivalent circuit.
30 V
1 A
Load the circuit with R2.
Calculate the load V and I.
110 V
20 W
10 W
30 W R2
1 A
30 V
7 A
8 A
Return to the original circuit and calculate the other currents.

7. Applying Norton’s Theorem to a Complex Circuit
Select a resistor to be the load.
Replace the load with a short.
Calculate the current through the short. This is IN.
Remove the short from the load terminals.
Replace all sources with shorts.
Calculate the resistance between the load terminals. This is RN.
Use IN and RN for the Norton circuit.
Connect the load to the Norton circuit.
Calculate Vload and Iload.

8. Equivalency of Norton and Thevenin Circuits
RTH
8 W
VTH
16 V - +
16 V V
The open-circuit
voltages RN
8 W IN
2 A
16 V V
are equal.
RTH
8 W
VTH
16 V - +
2 A A
The short-circuit
currents RN
8 W IN
2 A
2 A A
are equal.
When equally loaded,
RTH
8 W
VTH
16 V - + RN
8 W IN
2 A RL
24 W RL
24 W
the voltages
and currents
12 V
12 V
0.5 A
are equal.
0.5 A

9. Complex-Circuits Quiz
Which theorem(s) require(s) algebraically
adding the currents for each resistor? ____
Superposition
Which theorem(s) require(s) shorting all
voltage sources at the same time? ____
Thevenin
Norton
Which theorem(s) use(s) an equivalent-
circuit current source? ____
Norton
Which theorem(s) use(s) an equivalent-
circuit voltage source? ____
Thevenin
Which theorem(s) determine(s) the current
for all resistors in the circuit? ____
Superposition
The voltage of a(n) ____ voltage source is
independent of the load current.
ideal

10. REVIEW Superpositon Theorem Voltage Sources Thevenin’s Theorem
Norton’s Theorem