Question

When a coil is connected to a $100Vdc$ supply. The current is $2A$. When the same coil is connected to a.c. source $E=100\sqrt{2}\sin \omega t$, the current is $1A$. Find the inductive reactance used :

Answer 1

Given, $Voltage=100v,I=2A$

We know that in Dc circuit,

$I=\frac{v}{R}\Rightarrow R=\frac{V}{I}=\frac{100}{2}=50\Omega$

Or in the Ac circuit $I_{rms}=\frac{V_{rms}}{z}\Rightarrow 1=\frac{100}{z}\Rightarrow z=100\Omega$

Now,

$z=\sqrt{R^2+x_L^2}=\sqrt{{50}^2+x_L^2}=100\Rightarrow x_L=50\sqrt{3}$