An arc lamp requires a direct current of 10 A and 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:

1. 0.08 H
2. 0.044 H
3. 0.065 H
4. 80 H

Solution

For the lamp with direct current,

V = IR

R = 8 Ω

XL = Lω = L × (2πf) = L × 100π

$$Z = \sqrt{8^2+(L \times (100 \pi))^2}$$

$$Z = \dfrac{V_{rms}}{I_{rms}} = \dfrac{220}{10}$$

484 = 64 + 1042L2)

L = 0.065 H

The correct option is C.