Question

Calculate the resonant frequency and Q-factor (Quality factor) of a series L-C-R circuit containing a pure inductor of inductance 4 H, capacitor of capacitance $27\mu F$ and resistor of resistance $8\cdot 4\Omega$

Answer 1

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

$\therefore$ $w_o=\frac{1}{\sqrt{4\times 27\times {10}^{-6}}}$

$⟹$ $w_o=96.22Hz$

Quality factor $Q=\frac{L{w}_o}{R}$

$\therefore$ $Q=\frac{4\times 96.22}{8.4}$

$⟹$ $Q=45.82$