Question

When a series combination of inductance and resistance are connected with a $10V.50Hza.c$. source, a current of $1A$ flows in the circuit . The voltage leads the current by a phase angle of $\frac{\pi }{3}$ radian. Calculate the values of resistance and inductive reactance.

Answer 1

Inductive reactance $XL=\left|\omega L\right|$

as shown in phasor diagram.

$\tan \frac{\pi }{3}=\frac{I\times L}{IR}=\frac{\omega L}{R}=\sqrt{3}\omega L=\sqrt{3}R\to \left(1\right)$

Applying KVL

$jIXL+IR=10j\omega L+R=\frac{10}{i}=\frac{10}{7}=10\omega L+R=5\to \left(ii\right)$

From equation (ii) and (i)

$(\sqrt{3}+1)R=10R=\frac{5\times 2}{\sqrt{3}+1}=3.66\Omega \omega L=\sqrt{3}\times R=3.660\times \sqrt{3}L=\frac{6.330}{\omega }L=126.6mHL=0.126H$