Question

Calculate resonant frequency and Q-factor of a series L-C-R circuit containing a pure inductor of inductance 3 H, Capacitor of capacitance $27\mu F$ and resistor of resistance $7.4\Omega$.

Answer 1

Given : $L=3H$ $R=7.4\Omega$ $C=27\times {10}^{-6}F$

Resonant frequency $w_o=\frac{1}{\sqrt{LC}}$

$\therefore$ $w_o=\frac{1}{\sqrt{3\times 27\times {10}^{-6}}}$

$⟹$ $w_o=111.11$

Quality factor $Q=\frac{w_{o}L}{R}$

$\therefore$ $Q=\frac{111.11\times 3}{7.4}$

$⟹$ $Q=45.04$