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# 215+Ch8 - 8 AC POWER CIRCUITS by Ulaby Maharbiz Linear...

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8. AC POWER CIRCUITS by Ulaby & Maharbiz

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Linear Circuits at ac Instantaneous power Average power ) ( ) ( ) ( t i t t p υ = Power at any instant of time Average of instantaneous power over one period = T dt t p T P 0 ) ( 1 box2 Power delivery (utilities) box2 Electronics (laptops, mobile phones, etc.) box2 Logic circuits Power is critical for many reasons: Note: Power is not a linear function, cannot apply superposition
Instantaneous Power for Sinusoids Power depends on phases of voltage and current ( ) ( ) ( ) ( ) i i t t I V t p t i t t p t I t i t V t θ ω θ ω υ θ ω θ ω υ υ υ + + = = + = + = cos cos ) ( ) ( ) ( ) ( cos ) ( cos ) ( m m m m Trig. Identity:

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Average Value Sine wave
Average Value Truncated sawtooth

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Important Relation These properties hold true for positive integer values of n and any values of φ 1 and φ 2
Average Value for

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Effective or RMS Value Equivalent Value That Delivers Same Average Power to Resistor as in dc case For current given by Effective value is the (square) Root of the Mean of the Square of the periodic signal, or RMS value = = T T dt i T R dt R i T P 0 2 0 2 1 R I P 2 eff = ( ) ( ) t I t i ω cos m = Hence:

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215+Ch8 - 8 AC POWER CIRCUITS by Ulaby Maharbiz Linear...

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