Question

A 132 V ac source is connected to a pure inductor of inductance 140 mH. If the frequency of the ac source is 50 Hz, then the current passing through the inductor is

• A. 4 A
• B. 5 A
• C. 3 A
• D. 2 A

Hint:

For AC circuits with pure inductor, use $I = V / (2\pi f L)$. Convert mH to H by dividing by 1000. The current is RMS if voltage is RMS. Verify calculations with approximate $\pi = 3.14$ for quick estimates.

Answer 1

The Correct Option is C

1. In a pure inductive circuit, the current lags the voltage by 90 degrees, and the opposition to current is given by the inductive reactance $X_L$.
2. The inductive reactance is calculated as $X_L = 2\pi f L$, where $f$ is the frequency and $L$ is the inductance.
3. Given $f = 50$ Hz and $L = 140$ mH = 0.14 H, substitute: $X_L = 2 \times 3.1416 \times 50 \times 0.14 \approx 43.98 \, \Omega$.
4. The RMS current in the circuit is $I = \frac{V}{X_L}$, where $V = 132$ V is the RMS voltage.
5. Calculate $I = \frac{132}{43.98} \approx 3.00$ A. The value is exactly 3 A when using $\pi \approx 3.14$.
6. Therefore, the correct option is (3) 3 A.