63 AC power

# 63 AC power - EECS 314 Lecture notes AC Power Power in AC...

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© 2008 A. Ganago Power in AC Circuits In circuits with sinusoidal voltages, electric power can be calculated in many ways. Here we define the following power values: the instantaneous, average, RMS, complex, reactive, and apparent. All of them take into account the phase shift between voltage and current; the only exception is the apparent power. Except for the apparent power, all types of electric power are conserved. © 2008 A. Ganago Electric Power: The Basics Electric power is the product of voltage and current P = V · I Electric power is absorbed if P > 0 and supplied if P < 0 Energy is conserved at any moment of time thus the sum of electric powers absorbed by all circuit elements equals zero © 2008 A. Ganago Instantaneous Power At any moment of time, v(t)·i(t) = p(t) is the instantaneous power If the voltage v(t) and current i(t) change signs then the instantaneous power p(t) also can change its sign Some circuit elements can absorb power p(t)>0 at some intervals of time and supply power p(t)<0 at other intervals of time © 2008 A. Ganago Average Power The instantaneous power p(t) changes too fast; we seldom need to know it at all t If and are periodic (sinusoidal, etc.), in many applications, we focus on the integral of p(t) over the period = the average power P P = 1 T " p ( t ) dt , where T = 2 # \$ t 0 t 0 + T % = Period © 2008 A. Ganago Average Power: Sinusoidal • If v(t) = V m ·cos( ω · t + θ V ) and i(t) = I m ·cos( ω · t + θ I ) then the average power P can be expressed as: Note how important is the phase shift between the voltage and current ( θ V - θ I ) P = V m " I m 2 " cos( # V \$ # I ) © 2008 A. Ganago The Phase Shift If the phase shift between the voltage and current ( θ V - θ I ) = 0 then P = V m · I m / 2 • If ( θ V - θ I ) = ± π / 2 = ± 90º then P = 0 For any resistor, ( θ V - θ I ) = 0 thus P R > 0 For any capacitor, ( θ V - θ I ) = -90º thus P C = 0 For any inductor, ( θ V - θ I ) = 90º thus P L = 0

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