Question

A capacitor of unknown value and an inductor of $0.1H$ and a resistor of $10\Omega$ are connected in series to a $220V,50Hzac$ source. It is found that the power factor of circuit is unity. Calculate the capacitance of capacitor and maximum amplitude of current.

Answer 1

At resonant frequency, power factor the circuit is unity.

Resonant frequency $f_r=\frac{1}{2\pi \sqrt{LC}}$

Or $50=\frac{1}{2\pi \sqrt{0.1C}}$

$⟹C=100\mu F$

Also, at resonant frequency, $Z=R=10\Omega$

Rms current $I_{rms}=\frac{V}{Z}=\frac{220}{10}=22A$

Peak value of current $I_o=\sqrt{2}{I}_{rms}=\sqrt{2}\times 22=31.11A$