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Electrostatic Potential And Capacitance

Question
CBSEENPH12040059

In an AC circuit, the emf (e) and the current (i) at any instant are given respectively by

e = E0 sin ωt
i = Io sin (ωt -Φ)

The average power in the circuit over one cycle of AC is

  • fraction numerator straight E subscript straight o straight I subscript straight o over denominator 2 end fraction
  • fraction numerator straight E subscript straight o straight I subscript straight o over denominator 2 end fraction space sin space straight ϕ
  • fraction numerator straight E subscript straight o straight I subscript straight o over denominator 2 end fraction space cos space straight ϕ
  • EoIo

Solution

C.

fraction numerator straight E subscript straight o straight I subscript straight o over denominator 2 end fraction space cos space straight ϕ

The power is defined as the rate at which work is being done in the circuit.
Power = rate of work done in one complete cycle.
Or
Pav = W/T
straight P subscript av space equals fraction numerator left parenthesis straight E subscript straight o straight I subscript straight o space cos space straight ϕ right parenthesis space straight T divided by 2 over denominator straight T end fraction
straight P subscript av space equals space fraction numerator straight E subscript straight o straight I subscript straight o space cos space straight ϕ over denominator 2 end fraction
where cos Φ is called the power factor of an AC circuit.

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