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When a voltage v(S)=200sqrt2 sin (omega ...

When a voltage `v_(S)=200sqrt2 sin (omega t+15^(@))` is applied to an `AC` circuit the current in the circuit is found to be `i=2 sin (omegat+pi//4)` then average power concumed in the circuit is
(A)`200` watt , (B)`400sqrt2` watt , (C )`100sqrt6` watt , (D)`200sqrt2` watt

A

200watt

B

`400 sqrt(2)` watt

C

`100 sqrt(6)` watt

D

`200 sqrt(2)` watt

Text Solution

Verified by Experts

The correct Answer is:
C
Correction `150 to 15^(@)`
`P_(av)= v_(rms) I_(rms) cos phi`
`(200sqrt(2))/(sqrt2) = 2/(sqrt2) . Cos (30^(@)) = 200 sqrt(2) cos (15)`
`= 200sqrt(2)[1/(sqrt2)((sqrt(3))/2+1/2)]`
` = 200 [(sqrt(3)+1)/(2)] = 100 (sqrt(3)+1)`.
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