(B) The initial energy stored in the capacitor is $U_0 = \frac{1}{2} C V_0^2$.When $25\%$ of the energy is transferred to the inductor,the remaining e

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(B) The initial energy stored in the capacitor is $U_0 = \frac{1}{2} C V_0^2$.When $25\%$ of the energy is transferred to the inductor,the remaining energy in the capacitor is $U = U_0 - 0.25 U_0 = 0.75 U_0 = \frac{3}{4} U_0$.Since the energy stored in a capacitor is given by $U = \frac{1}{2} C V^2$,we have $\frac{1}{2} C V^2 = \frac{3}{4} (\frac{1}{2} C V_0^2)$.Simplifying this,we get $V^2 = \frac{3}{4} V_0^2$.Taking the square root of both sides,we find $V = \frac{\sqrt{3}}{2} V_0$.

Class 12 Physics Alternating Current LC Oscillations

Medium

$A$ capacitor of capacitance $C$ is charged to a potential difference $V_0$. Now,this capacitor is connected to an ideal inductor. When $25\%$ of the energy of the capacitor is transferred to the inductor,what will be the potential difference across the capacitor?

A
$\frac{V_0}{2}$
B
$\frac{\sqrt{3}}{2} V_0$
C
$\frac{V_0}{4}$
D
$\frac{V_0}{\sqrt{3}}$

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Alternating Current

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LC Oscillations

$A$ capacitor of capacity $20 \mu F$ is charged to a potential of $35 \text{ V}$. The battery is then disconnected. $A$ pure inductor coil of $200 \text{ mH}$ is connected across the capacitor so that $LC$ oscillations are set up. The maximum current in the coil is: (in $\text{ A}$)

MediumMHT CET 2022

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In an $LC$ oscillator,if values of inductance and capacitance become twice and eight times,respectively,then the resonant frequency of the oscillator becomes $x$ times its initial resonant frequency $\omega_0$. The value of $x$ is:

EasyJEE MAIN 2023

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Show that in the free oscillations of an $LC$ circuit,the sum of energies stored in the capacitor and the inductor is constant in time.

Medium

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$A$ capacitor of capacitance $C$ has an initial charge $Q_0$ and is connected to an inductor $L$ as shown. At $t = 0$,the switch $S$ is closed. What is the current through the inductor when the energy in the capacitor is three times the energy of the inductor?

Easy

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$A$ $1 \, \mu F$ capacitor is charged to $50 \, V$. The charging battery is then disconnected and a $10 \, mH$ coil is connected across the capacitor so that $LC$ oscillations occur. What is the maximum current in the coil (in $, A$)? Assume that the circuit contains no resistance.

DifficultMHT CET 2022

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$A$ capacitor of capacitance $C$ is charged to a potential difference $V_0$. Now,this capacitor is connected to an ideal inductor. When $25\%$ of the energy of the capacitor is transferred to the inductor,what will be the potential difference across the capacitor?

Similar Questions

$A$ capacitor of capacity $20 \mu F$ is charged to a potential of $35 \text{ V}$. The battery is then disconnected. $A$ pure inductor coil of $200 \text{ mH}$ is connected across the capacitor so that $LC$ oscillations are set up. The maximum current in the coil is: (in $\text{ A}$)

In an $LC$ oscillator,if values of inductance and capacitance become twice and eight times,respectively,then the resonant frequency of the oscillator becomes $x$ times its initial resonant frequency $\omega_0$. The value of $x$ is:

Show that in the free oscillations of an $LC$ circuit,the sum of energies stored in the capacitor and the inductor is constant in time.

$A$ capacitor of capacitance $C$ has an initial charge $Q_0$ and is connected to an inductor $L$ as shown. At $t = 0$,the switch $S$ is closed. What is the current through the inductor when the energy in the capacitor is three times the energy of the inductor?

$A$ $1 \, \mu F$ capacitor is charged to $50 \, V$. The charging battery is then disconnected and a $10 \, mH$ coil is connected across the capacitor so that $LC$ oscillations occur. What is the maximum current in the coil (in $, A$)? Assume that the circuit contains no resistance.

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