Question

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

Answer 1

Phase difference between current and voltage $\varphi =\frac{\pi }{3}$
Rms value of source voltage $V_{rms}=10V$
Rms value of current $I_{rms}=1A$
Thus impedance of circuit $Z=\frac{V_{rms}}{I_{rms}}=\frac{10}{1}=10\Omega$
Using $\cos \varphi =\frac{R}{Z}$
We get $\cos \frac{\pi }{3}=\frac{R}{10}$
$⟹R=5\Omega$
Also using $\tan \varphi =\frac{X_L}{R}$
$\therefore$ $\tan \frac{\pi }{3}=\frac{X_L}{5}$
$⟹X_L=5\sqrt{3}\Omega$