Principles & Applications Complex-Circuit Analysis Electricity Principles & Applications Sixth Edition Richard J. Fowler Chapter 6 Complex-Circuit Analysis ©2003 Glencoe/McGraw-Hill

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

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.

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.

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.

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.

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.

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

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

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