Ncert Exercises & Solutions

Question 7.6 :

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

Given:

The inductance of the inductor is L = 2.0 H

The capacitance of the capacitor, C = 32 μF = 32 × 10 ^{– 6} F

The resistance of the resistor is R = 10 Ω.

We know that the resonant frequency can be calculated by the following relation,

$\begin{array}{l} à ω_{r} = \frac{1}{\sqrt{L C}} = \frac{1}{\sqrt{2 \times 32 \times 10^{- 6}}} = \frac{1}{8 \times 10^{- 3}} \\ = 125 \frac{rad}{sec} \end{array}$

Now, Q – value of the circuit can be calculated as follows :

$\begin{array}{l} à Q = \frac{1}{R} \sqrt{\frac{l}{c}} = \frac{1}{10} \sqrt{\frac{2}{32 \times 10^{6}}} \\ = \frac{1}{10 \times 4 \times 10^{- 3}} = 25 \end{array}$

Thus, the Q – Value of the above question is 25.

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