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Question

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

Vedclass · Accepted Answer

$1.1 	imes 10^3\,rad\,s^{-1}$

Vedclass · Answer

(A) Given:Capacitance $C = 30\,\mu F = 30 	imes 10^{-6}\,F$Inductance $L = 27\,mH = 27 	imes 10^{-3}\,H$The angular frequency $\omega$ of free oscillations in an $LC$ circuit is given by the formula:$\omega = \frac{1}{\sqrt{LC}}$Substituting the values:$\omega = \frac{1}{\sqrt{(27 	imes 10^{-3}) 	imes (30 	imes 10^{-6})}}$$\omega = \frac{1}{\sqrt{810 	imes 10^{-9}}}$$\omega = \frac{1}{\sqrt{81 	imes 10^{-8}}}$$\omega = \frac{1}{9 	imes 10^{-4}}$$\omega = \frac{10^4}{9} \approx 1.11 	imes 10^3\,rad\,s^{-1}$Thus,the angular frequency is $1.1 	imes 10^3\,rad\,s^{-1}$.

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

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