Question

In a series $L R$ 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 $3 V$ and voltage across the resistance is $4\, V$. If resistance is $2 \,\Omega$, what is the reactance (in $\Omega$ ) of the inductor?

Answer 1

$V_{L}=i_{0} X_{L} \sin (\omega t+90-\phi)$
$V_{R}=i_{0} R \sin (\omega t-\phi)$
$V=V_{0} \sin (\omega t)$
$3=V_{L}=i_{0} X_{L} \sin \phi$
$4=V_{R}=i_{0} R \cos \phi$
$\frac{3}{4}=\frac{\omega L}{R} \tan \phi=\frac{\omega^{2} L^{2}}{R^{2}}$
$\Rightarrow \frac{\omega L}{R}=\frac{\sqrt{3}}{2}$
$ \Rightarrow X_{L}=\sqrt{3} \Omega$