Question

Obtain the resonant frequency ${\omega }_r$ of a series LCR circuit with L = 2.0 H, C = 32 $\mu$F and R = 10 $\Omega$. What is the Q-value of this circuit?

Answer 1

Given: The inductance in the circuit is $2.0H$.

The capacitance in the circuit is $32\mu F$.

The resistance in the circuit is $10\Omega$.

To find: The resonant frequency and Q-value of the circuit.

The resonant frequency is given by

${\omega }_r=\frac{1}{\sqrt{LC}}=\frac{1}{\sqrt{2\times 32\times {10}^{-6}}}$

$\Rightarrow 125rad/s$

The Q value of the circuit is given by:

$Q=\frac{1}{R}\sqrt{\frac{L}{C}}=\frac{1}{10}\sqrt{\frac{2}{32\times {10}^{-6}}}$

$\Rightarrow Q=25$