Power in an AC Circuit Class 12 Notes | EduRev

Physics Class 12

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Class 12 : Power in an AC Circuit Class 12 Notes | EduRev

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7. Power in an AC circuit

In case of a steady current the rate of doing work is given by,

P = Vi

In an alternating circuit, current and voltage both vary with time, so the work done by the source in time interval dt is given by

dW= Vidt

Suppose in an ac, the current is leading the voltage by an angle φ. Then we can write,

V = V0 sinωt

and = i0 sin(ωt + φ)

dW = V0i0 sin ωt sin (ωt + φ) dt

= V0 i0 (sin2 ωt cos f + sinωt cos ωt sin φ) dt

The total work done in a complete cycle is

W = V0i0 cosPower in an AC Circuit Class 12 Notes | EduRevPower in an AC Circuit Class 12 Notes | EduRev + V0i0sinPower in an AC Circuit Class 12 Notes | EduRev

Power in an AC Circuit Class 12 Notes | EduRevPower in an AC Circuit Class 12 Notes | EduRev = Power in an AC Circuit Class 12 Notes | EduRev

The average power delivered by the source is, therefore,

P = Power in an AC Circuit Class 12 Notes | EduRev = Power in an AC Circuit Class 12 Notes | EduRev = Power in an AC Circuit Class 12 Notes | EduRev

= Vrms irms cos φ

or <P>one cycle = Vrms irms cos φ

Here, the term cos φ is known as power factor.

It is said to be leading if current leads voltage, lagging if current lags voltage. Thus, a power factor of 0.5 lagging means current lags the voltage by 60° (as cos-10.5 = 60°). The product of Vrms and irms gives the apparent power. While the true power is obtained by multiplying the apparent power by the power factor cos φ. Thus,

and apparent power = Vrms × irms

True power = apparent power × power factor

For φ= 0°, the current and voltage are in phase. The power is thus, maximum (Vrms× irms). For

φ = 90°, the power is zero. The current is then stated as wattless. Such a case will arise when resistance in the circuit is zero. The circuit is purely inductive or capacitive.

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