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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+b22The 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, 1T∫T0sinωtdt=0 and 1T∫T0sin2ωtdt=12 ∴Ieff=√∫T0a2dtT+∫T0b2dt2T=√a2+b22 Hence, option (C) is correct answer.

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