Question

An inductor of reactance \(1\,\Omega\) and a resistor of resistance \(3\,\Omega\) are connected in series to the terminals of \(10\,\text{V}\) (rms) ac source. The power dissipated in the circuit is

• A. \(33.3\,\text{W}\)
• B. \(30\,\text{W}\)
• C. \(31.6\,\text{W}\)
• D. \(20\,\text{W}\)

Hint:

In an \(RL\) circuit, only the resistor dissipates real power: \[ P=I_{\text{rms}}^2R. \] The inductor stores and releases energy but does not dissipate average power.

Answer 1

The Correct Option is B

Step 1: Calculate circuit impedance.
Z = √(R² + X_L²) = √(3² + 1²) = √10 Ω.

Step 2: Find r.m.s. current.
I_rms = V_rms/Z = 10/√10 = √10 A.

Step 3: Compute power dissipated (only in resistor).
P = I_rms² R = 10 × 3 = 30 W.

Step 4: Final Answer:
30 W.