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Lecture 3: Resistive Circuits Nilsson & Riedel 3.1-3.4, 3.7 ENG17 (Sec. 2): Circuits I Spring 2014 1 April 8, 2014

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

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

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

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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

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

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Voltage Divider One voltage supply, multiple voltage levels 7

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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

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Example 9

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

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Current Divider 11 One current supply, multiple current levels

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Example 12

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

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Voltage Division 14 Generalization of voltage divider circuit

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Current Division 15 Generalization of current divider circuit

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Example 16

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

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

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Defining Delta/Pi and Y/T 19 Δ Y T π

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

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Apply to Wheatstone Bridge 21

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Rear Window Defroster 22

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

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

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