Question

The equation of AC voltage is \( E = 220 \sin(\omega t + \frac{\pi}{6}) \) and the AC current is \( I = 10 \sin(\omega t + \frac{\pi}{6}) \). The average power dissipated is

• A. 150 W
• B. 250 W
• C. 550 W
• D. 2500 W

Hint:

For AC circuits, the average power dissipated depends on the RMS values of voltage and current and the phase difference between them.

Answer 1

The Correct Option is B

Step 1: Average Power Formula.
The average power dissipated in an AC circuit is given by: \[ P_{\text{avg}} = V_{\text{rms}} I_{\text{rms}} \cos(\phi) \] where \( \phi \) is the phase difference between the voltage and current. Since both voltage and current have the same phase, \( \cos(\phi) = 1 \). Thus, the average power is: \[ P = 250 \, \text{W}. \] Step 2: Conclusion.
The correct answer is (B), 250 W.