Lecture 3: Resistive Circuits Nilsson & Riedel , 3.7 ENG17 (Sec. 2): Circuits I Spring April 8, 2014

Overview Resistors in Series Resistors in Parallel Voltage Divider Current Divider Voltage / Current Division Δ-to-Y Equivalent Circuits 2

Series Connected Elements Resistors in series carry the same current –KCL proves this Resistors in series can be summed –KVL proves this 3

Overview Resistors in Series Resistors in Parallel Voltage Divider Current Divider Voltage / Current Division Δ-to-Y Equivalent Circuits 4

Parallel Connected Elements Resistors in parallel have same voltage across their terminals –KVL proves this Resistors in parallel can be summed inversely –KCL proves this –Conductances are summed 5

Overview Resistors in Series Resistors in Parallel Voltage Divider Current Divider Voltage / Current Division Δ-to-Y Equivalent Circuits 6

Voltage Divider One voltage supply, multiple voltage levels 7

Load R L = load = 1+ circuit elements that draw power from circuit –May alter voltage across parallel element –But not if R L >> R 2 8

Example 9

Overview Resistors in Series Resistors in Parallel Voltage Divider Current Divider Voltage / Current Division Δ-to-Y Equivalent Circuits 10

Current Divider 11 One current supply, multiple current levels

Example 12

Overview Resistors in Series Resistors in Parallel Voltage Divider Current Divider Voltage / Current Division Δ-to-Y Equivalent Circuits 13

Voltage Division 14 Generalization of voltage divider circuit

Current Division 15 Generalization of current divider circuit

Example 16

Overview Resistors in Series Resistors in Parallel Voltage Divider Current Divider Voltage / Current Division Δ-to-Y Equivalent Circuits 17

Unable to get R eq For example, Wheatstone bridge circuit (below) cannot be simplified with standard parallel/series rules Must use circuit transformation 18

Defining Delta/Pi and Y/T 19 Δ Y T π

Delta-to-Wye Circuit Transformation Equivalent resistance between nodes Note: resistor values are NOT THE SAME 20

Apply to Wheatstone Bridge 21

Rear Window Defroster 22

Rear Window Defroster - Problem Need: Power dissipated per unit length is same in each conductor 23

Recap Resistors in Series Resistors in Parallel Voltage Divider Current Divider Voltage / Current Division Δ-to-Y Equivalent Circuits 24