Ncert Exercises & Solutions

Question 7.7 :

A charged 30 µF capacitor is connected to a 27 mH inductor. What is the angular frequency of free oscillations of the circuit?

Given Capacitance value of the capacitor , C = 30 μF = 30 × 10 ^{– 6} F

Given Inductance value of the charged inductor, L = 27 mH = 27 × 10 ^{– 3} H

Angular frequency is given as :

\begin{array}{l} \dot{a} ω_{r} = \frac{1}{\sqrt{L C}} \\ \dot{a} ω_{r} = \frac{1}{\sqrt{27 \times 10^{- 3} \times 30 \times 10^{- 6}}} = \frac{1}{9 \times 10^{- 4}} = 1.11 \times 10^{3} \frac{r a d}{s e c} \end{array}

Therefore , the calculated angular frequency of free oscillation of the connection is 1.11 x 10 ³ rad / s