Question

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

Answer 1

Given : $V_{rms}=10V$ $I_{rms}=1A$ $\varphi =\frac{\pi }{3}$ $f=50Hz$

Impedance $Z=\frac{V_{rms}}{I_{rms}}=\frac{10}{1}=10\Omega$

Using $\cos \varphi =\frac{R}{Z}$

Or $\cos \frac{\pi }{3}=\frac{R}{10}$ $⟹R=5\Omega$

Using $Z^2=R^2+(2\pi fL{)}^2$

Or ${10}^2=5^2+(2\pi \times 50\times L{)}^2$

$⟹L=28mH$