Question

A $15$ $\Omega$ resistor, an $80\text{mH}$ inductor and a capacitor of capacitance $C$ are connected in series with a $50\text{Hz}$ ac source. If the source voltage and current in the circuit are in phase, then the value of capacitance is

Answer 1

As voltage and current are in phase –

$\varphi =0$

This means circuit is in resonance.

$\Rightarrow \omega =\frac{1}{\sqrt{LC}}$

$\Rightarrow C=\frac{1}{{\omega }^{2}L}=\frac{1}{(100\pi {)}^2\times 800\times {10}^{-3}}\Rightarrow C=127\mu F$