Post on 24-Dec-2015
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Lecture 3:Resistive CircuitsNilsson & Riedel 3.1-3.4, 3.7
ENG17 (Sec. 2): Circuits I
Spring 2014
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
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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
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Overview
• Resistors in Series• Resistors in Parallel• Voltage Divider• Current Divider• Voltage / Current
Division• Δ-to-Y Equivalent
Circuits
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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
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Overview
• Resistors in Series• Resistors in Parallel• Voltage Divider• Current Divider• Voltage / Current
Division• Δ-to-Y Equivalent
Circuits
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Voltage Divider
• One voltage supply, multiple voltage levels
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Load
• RL = load = 1+ circuit elements that draw power from circuit– May alter voltage across parallel element
– But not if RL >> R2
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Example
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Overview
• Resistors in Series• Resistors in Parallel• Voltage Divider• Current Divider• Voltage / Current
Division• Δ-to-Y Equivalent
Circuits
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Current Divider
• One current supply, multiple current levels
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Example
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Overview
• Resistors in Series• Resistors in Parallel• Voltage Divider• Current Divider• Voltage / Current
Division• Δ-to-Y Equivalent
Circuits
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Voltage Division
• Generalization of voltage divider circuit
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Current Division
• Generalization of current divider circuit
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Example
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Overview
• Resistors in Series• Resistors in Parallel• Voltage Divider• Current Divider• Voltage / Current
Division• Δ-to-Y Equivalent
Circuits
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Unable to get Req
• For example, Wheatstone bridge circuit (below) cannot be simplified with standard parallel/series rules
• Must use circuit transformation
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Defining Delta/Pi and Y/T
Δ
Y T
π
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Delta-to-Wye Circuit Transformation
• Equivalent resistance between nodes• Note: resistor values are NOT THE SAME
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Apply to Wheatstone Bridge
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Rear Window Defroster
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Rear Window Defroster - Problem
• Need: Power dissipated per unit length is same in each conductor
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Recap
• Resistors in Series• Resistors in Parallel• Voltage Divider• Current Divider• Voltage / Current
Division• Δ-to-Y Equivalent
Circuits