Electrical Systems

Power in AC Circuit

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V and I are the rms values of voltage and current

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(-ve value of φ means current lags voltage)

Average Power is P

P = VI cos(φ) Dummy Text

p is the instantaneous power

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v is the sinusoidal voltage

i is the sinusoidal current due to voltage v

φ is the phase angle between v and i sinusoid


i= I msin(ωt + φ)

The instantaneous power is given as p  =   v.i

p  =   Vmsin(ωt) . Imsin(ωt + φ)

On simplification we get

p  =   Vm Im 2 cos(φ) - Vm Im 2 cos(2ωt + φ)

The first term is constant for a given load and the second term is a sinusoid of frequency 2ω

In one cycle the net value of the second term is zero. The first term is the average power

The average power  =   Vm Im 2 cos(φ) P  =   VI  cos(φ)

P is the average power and V & I are rms values

The average power is also known as real power.