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Electrostatic Potential And Capacitance

Question
CBSEENPH12039828
Wired Faculty App

The instantaneous values of alternating current and voltages in a circuit are given as

straight i space equals space fraction numerator 1 over denominator square root of 2 end fraction space sin space left parenthesis 100 πt right parenthesis space ampere straight e space equals fraction numerator 1 over denominator square root of 2 space end fraction space sin space left parenthesis 100 πt space plus straight pi over 3 right parenthesis space volt
The average power in Watts consumed in the circuit is

  • 1/4

  • fraction numerator square root of 3 over denominator 4 end fraction

  • 1/2

  • 1/8

Solution

D.

1/8

Given equations
straight i space equals fraction numerator 1 over denominator square root of 2 end fraction space sin space left parenthesis 100 πt right parenthesis and space straight e equals fraction numerator 1 over denominator square root of 2 end fraction sin space left parenthesis 100 straight pi space straight t plus straight pi divided by 3 right parenthesis therefore straight i subscript straight o space equals fraction numerator 1 over denominator square root of 2 space end fraction space and space straight v subscript straight o space equals fraction numerator 1 over denominator square root of 2 end fraction We space know space that space average space power straight P subscript av space equals straight V subscript rms straight x space straight i subscript rms cosϕ space equals space 1 half space straight x 1 half space straight x space cos 60 to the power of straight o open square brackets therefore space straight i subscript rms space equals fraction numerator straight i subscript straight o over denominator square root of 2 end fraction space and space straight v subscript rms space equals space fraction numerator straight V subscript straight o over denominator square root of 2 end fraction close square brackets space equals space fraction numerator 1 over denominator 2 space end fraction space straight x space 1 half space straight x space 1 half space equals space 1 over 8 straight W

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