Question

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

• A. $0.08\text{H}$
• B. $0.044\text{H}$
• C. $0.065\text{H}$
• D. $80\text{H}$

Answer 1

The correct option is C $0.065\text{H}$

Potential across lamp for lamp to work $I=10A,V_R=80V$
We know that
$V_L^2+V_R^2={220}^2$
$V_L^2+6400=220\times 220$
$V_L=\sqrt{48400-6400}=205V$

$V_L=I{X}_L=205$
i.e $I\times 2\pi fL=205$
i.e $L=\frac{205}{10\times 100\pi }=0.065\text{H}$