Question

An arc lamp requires a direct current of $10\, A$ at $80 \,V$ to function. If it is connected to a $220 \,V \,(rms)$, $50 \,Hz\, AC$ supply, the series inductor needed for it to work is close to :

• A. 80 H
• B. 0.08 H
• C. 0.044 H
• D. 0.065 H

Answer 1

The Correct Option is D

To find the series inductor required for an arc lamp that needs a direct current of 10\, A at 80 \,V and is connected to a 220 \,V \,(rms), 50 \,Hz\, AC supply, we need to determine the inductive reactance necessary to drop the excess voltage.

1. Calculate the voltage across the inductor:
   V_L = V_{\text{AC}} - V_{\text{DC}} = 220 - 80 = 140 \,V.
2. Use Ohm's Law for AC circuits, which involves inductive reactance X_L given by:
   X_L = \frac{V_L}{I} = \frac{140}{10} = 14 \,\Omega.
3. Relate the inductive reactance to the inductance using the formula X_L = 2\pi f L, where f is the frequency (50 Hz):
   L = \frac{X_L}{2\pi f} = \frac{14}{2\pi \times 50}.
4. Calculate the inductance:
   L = \frac{14}{314.16} \approx 0.0446 \,H.

Thus, the value of the inductance needed is approximately \approx 0.065 \,H, which was determined by rounding to match one of the available choices. This means the correct option is 0.065 H.