Question

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

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

Answer 1

The correct option is D $0.065H$

Resistance of lamp by Ohm's law,
$R=\frac{V}{I}=\frac{80}{10}=8\Omega$

When inductor is connected in series and source is applied,
$V=IZ$
$V=I\sqrt{R^2+(\omega L{)}^2}$
Given, $I=10A$ for lamp to work,
$220=10\sqrt{8^2+(2\times \pi \times 50\times L{)}^2}$
Solving,
$L=0.0648H$