Question

In a series $LR$ circuit connected to an alternating voltage source, it is observed that at the instant voltage across the source is maximum, voltage across the inductor is $3V$ and voltage across the resistance is $4V$. If resistance is $2\Omega$, what is the reactance (in $\Omega$ ) of the inductor?

Answer 1

Answer: 1.73

$V_L=i_0{X}_L\sin (\omega t+90-\varphi )$
$V_R=i_{0}R\sin (\omega t-\varphi )$
$V=V_0\sin (\omega t)$
$3=V_L=i_0{X}_L\sin \varphi$
$4=V_R=i_{0}R\cos \varphi$
$\frac{3}{4}=\frac{\omega L}{R}\tan \varphi =\frac{{\omega }^2{L}^2}{R^2}$
$\Rightarrow \frac{\omega L}{R}=\frac{\sqrt{3}}{2}$
$\Rightarrow X_L=\sqrt{3}\Omega$