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

Explanation

To solve the problem of finding the average power consumed in the AC circuit, we can follow these steps:

### Step 1: Identify the peak voltage and peak current
The given voltage is:
\[ v_S = 200\sqrt{2} \sin(\omega t + 15^\circ) \]
From this, we can identify the peak voltage \( V_0 \):
\[ V_0 = 200\sqrt{2} \]

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