Obtain the resonant frequency
Question:

Obtain the resonant frequency ωof a series LCR circuit with = 2.0 H, = 32 μF and = 10 Ω. What is the Q-value of this circuit?

Solution:

Inductance, = 2.0 H

Capacitance, C = 32 μF = 32 × 10−6 F

Resistance, R = 10 Ω

Resonant frequency is given by the relation,

$\omega_{\mathrm{r}}=\frac{1}{\sqrt{L C}}$

$=\frac{1}{\sqrt{2 \times 32 \times 10^{-6}}}=\frac{1}{8 \times 10^{-3}}=125 \mathrm{~s}^{-1}$

Now, Q-value of the circuit is given as:

$Q=\frac{1}{R} \sqrt{\frac{L}{C}}$

$=\frac{1}{10} \sqrt{\frac{2}{32 \times 10^{-6}}}=\frac{1}{10} \times \frac{1}{4 \times 10^{-3}}=25$

Hence, the Q-Value of this circuit is 25.

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