Question

Find the value of an inductance $\left(\text{in H}\right)$ which should be connected in series with a capacitor of $5\mu \text{F}$, a resistance of $10\Omega$ and a source of $50/\pi \text{Hz}$ so that the power factor of the circuit is unity.

Answer 1

Given:-
Frequency, $f=50/\pi \text{Hz}$

Capacitance, $C=5\mu \text{F}$

Resistance, $R=10\Omega$

Now, $\omega =2\pi f=100$

For, Power factor $=1$

$\Rightarrow \frac{R}{Z}=1$

$\Rightarrow R=Z$

$\Rightarrow X_L=X_C$

$\Rightarrow \omega L=\frac{1}{\omega C}$

$\Rightarrow L=\frac{1}{{\omega }^{2}C}$

$=\frac{1}{{10}^4\times 5\times {10}^{-6}}$

$\therefore L=20\text{H}$