Question

A voltage \( v = v_0 \sin(\omega t) \) applied to a circuit drives a current \( i = i_0 \sin(\omega t + \varphi) \) in the circuit. The average power consumed in the circuit over a cycle is:

• A. Zero
• B. \( i_0 v_0 \cos \varphi \)
• C. \( \frac{i_0 v_0}{2} \)
• D. \( i_0 v_0 \cos \varphi \)

Hint:

The average power in an AC circuit is the product of the RMS values of voltage and current and the cosine of the phase difference.

Answer 1

The Correct Option is B

The average power consumed in an AC circuit is given by: \[ P_{\text{avg}} = \frac{1}{T} \int_0^T v(t) \cdot i(t) \, dt \] For sinusoidal voltage and current: \[ P_{\text{avg}} = \frac{1}{2} i_0 v_0 \cos \varphi \] Thus, the correct answer is \( i_0 v_0 \cos \varphi \).