An LC circuit contains a 20 , mH inductor and | vedclass

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(B) Given: Inductance $L = 20 \, mH = 20 	imes 10^{-3} \, H$,Capacitance $C = 50 \, \mu F = 50 	imes 10^{-6} \, F$.The angular frequency of the $LC$

Vedclass · Accepted Answer

$1.57$

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(B) Given: Inductance $L = 20 \, mH = 20 	imes 10^{-3} \, H$,Capacitance $C = 50 \, \mu F = 50 	imes 10^{-6} \, F$.The angular frequency of the $LC$ circuit is $\omega = \frac{1}{\sqrt{LC}}$.The time period of oscillation is $T = 2\pi \sqrt{LC}$.Initially,at $t = 0$,the energy is stored entirely in the electric field of the capacitor. The energy oscillates between the electric field of the capacitor and the magnetic field of the inductor.The energy stored is completely magnetic at $t = \frac{T}{4}, \frac{3T}{4}, \dots$Calculating the first instance $t = \frac{T}{4} = \frac{2\pi \sqrt{LC}}{4} = \frac{\pi}{2} \sqrt{LC}$.Substituting the values: $t = \frac{3.14}{2} \sqrt{20 	imes 10^{-3} 	imes 50 	imes 10^{-6}} = 1.57 	imes \sqrt{1000 	imes 10^{-9}} = 1.57 	imes \sqrt{10^{-6}} = 1.57 	imes 10^{-3} \, s$.Thus,$t = 1.57 \, ms$.

An $LC$ circuit contains a $20 \, mH$ inductor and a $50 \, \mu F$ capacitor with an initial charge of $10 \, mC$. The resistance of the circuit is negligible. Let the instant the circuit is closed be $t = 0$. At what time is the energy stored completely magnetic? $t = \dots \, ms$

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