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(B) Given:Capacitance $C = 30\; \mu F = 30 	imes 10^{-6}\; F$Inductance $L = 27\; mH = 27 	imes 10^{-3}\; H$The angular frequency of free oscillatio

Vedclass · Accepted Answer

$1.11 	imes 10^{3}\; rad/s$

Vedclass · Answer

(B) Given:Capacitance $C = 30\; \mu F = 30 	imes 10^{-6}\; F$Inductance $L = 27\; mH = 27 	imes 10^{-3}\; H$The angular frequency of free oscillations $\omega_r$ for an $LC$ circuit is given by the formula:$\omega_r = \frac{1}{\sqrt{LC}}$Substituting the values:$\omega_r = \frac{1}{\sqrt{27 	imes 10^{-3} 	imes 30 	imes 10^{-6}}}$$\omega_r = \frac{1}{\sqrt{810 	imes 10^{-9}}}$$\omega_r = \frac{1}{\sqrt{8.1 	imes 10^{-7}}} = \frac{1}{\sqrt{810 	imes 10^{-9}}} = \frac{1}{900 	imes 10^{-6}} = \frac{1}{9 	imes 10^{-4}}$$\omega_r = \frac{10^4}{9} \approx 1.11 	imes 10^3\; rad/s$Thus,the angular frequency of free oscillations of the circuit is $1.11 	imes 10^3\; rad/s$.

$A$ charged $30\; \mu F$ capacitor is connected to a $27\; mH$ inductor. What is the angular frequency of free oscillations of the circuit?

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