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12 - AC Power

# 12 - AC Power - EECS 215 AC Power Instantaneous And Average...

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EECS 215 AC Power J. Phillips EECS 215 Instantaneous And Average Power Need to know where power is going in a circuit Instantaneous power Average power ) ( ) ( ) ( t i t v t p = power at any instant of time average of instantaneous power over one period = T dt t p T P 0 ) ( 1 Power delivery (utilities) Electronics (laptops, mobile phones, etc) Logic circuits Power is critical for many areas Note: power is not a linear function, cannot apply superposition

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J. Phillips EECS 215 Instantaneous Power For Sinusoids Power depends on phase of voltage and current ( ) ( ) ( ) ( ) i v m m i m v m t t I V t p t i t v t p t I t i t V t v θ ω θ ω θ ω θ ω + + = = + = + = cos cos ) ( ) ( ) ( ) ( cos ) ( cos ) ( ( ) ( ) ( ) ( ) [ ] B A B A B A + + = cos cos 2 1 cos cos ( ) ( ) [ ] i v i v m m t I V t p θ θ ω θ θ + + + = 2 cos cos 2 1 ) ( Trig. Identity: Constant in time AC at 2 ω J. Phillips EECS 215 Average Power ) ( ) ( ) ( t i t v t p = = T dt t p T P 0 ) ( 1 ( ) ( ) v m t V t v θ ω + = cos ( ) ( ) i m t I t i θ ω + = cos ( ) i v m m ave I V P θ θ = cos 2 1 ( ) * Re 2 1 VI P ave = Note that phase is important Resistive load absorbs power at all times Reactive load absorbs zero power ( ) i v m m I V θ θ cos 2 1
J. Phillips EECS 215

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