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Question

If a direct current of value a ampere is superimposed on an alternating current I=bsinωt flowing through a wire, what is the effective value of the resulting current in the circuit?

A
a2+b2
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B
a2+b24
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C
a2+b22
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D
a22+b2
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Solution

The correct option is C a2+b22
The total current at any instant in the circuit will be,

I=IDC+IAC=a+bsinωt

Ieff=Irms=T0I2dtT

=T0(a+bsinωt)2dtT

=T0(a2+2absinωt+b2sin2ωt)dtT

=T0a2dt+T02absinωt dt+T0b2sin2ωt dtT

As,
1TT0sinωtdt=0 and 1TT0sin2ωtdt=12

Ieff=T0a2dtT+T0b2dt2T=a2+b22

Hence, option (C) is correct answer.

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