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

Answer: (D)

0.065 H

Answer 2

For $dc$

$R = \frac{80}{10} = 8 \omega$
For $ac$

$10 = \frac{220}{\sqrt{R^{2} + \omega^{2}L^{2}}}$
$R^{2} + \omega^{2}L^{2} = \left(\frac{220}{10}\right)^{2}$
$L^{2} = \frac{22^{2} - 8^{2}}{\omega^{2}}$
$\therefore L = \frac{\sqrt{30 \times14}}{2 \pi\times50} = \frac{\sqrt{420}}{100 \pi} = 0.065\, H$