Question

Voltage and current in an AC circuit are given by \(V = 50\sin(50t)\,\text{V}\) and \(i = 50\sin(50t + \frac{\pi}{3})\,\text{mA}\). The power dissipated in the circuit is:

• A. \(5.0\,\text{W}\)
• B. \(2.5\,\text{W}\)
• C. \(1.25\,\text{W}\)
• D. zero

Hint:

Always convert peak values to RMS before calculating AC power.

Answer 1

The Correct Option is C

Step 1: Average power: \[ P = V_{\text{rms}} I_{\text{rms}} \cos\phi \]
Step 2: \[ V_{\text{rms}} = \frac{50}{\sqrt{2}},\quad I_{\text{rms}} = \frac{0.05}{\sqrt{2}} \]
Step 3: \[ P = \frac{50 \times 0.05}{2} \cos\frac{\pi}{3} = 1.25\,\text{W} \]