A capacitor of capacity C is charged to a pot | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) According to the principle of conservation of energy in an $LC$ circuit,the total energy remains constant.Initial energy stored in the capacitor i

Vedclass · Accepted Answer

$[\frac{C(V_1^2 - V_2^2)}{L}]^{1/2}$

Vedclass · Answer

(D) According to the principle of conservation of energy in an $LC$ circuit,the total energy remains constant.Initial energy stored in the capacitor is $U_i = \frac{1}{2} C V_1^2$.When the potential difference across the capacitor is $V_2$,the energy stored in the capacitor is $U_c = \frac{1}{2} C V_2^2$.The remaining energy is stored in the inductor as magnetic energy,$U_L = \frac{1}{2} L I^2$.By conservation of energy: $\frac{1}{2} C V_1^2 = \frac{1}{2} C V_2^2 + \frac{1}{2} L I^2$.Rearranging for $I^2$: $L I^2 = C(V_1^2 - V_2^2)$.Thus,$I^2 = \frac{C(V_1^2 - V_2^2)}{L}$.Therefore,the current is $I = [\frac{C(V_1^2 - V_2^2)}{L}]^{1/2}$.

$A$ capacitor of capacity $C$ is charged to a potential difference of $V_1$. The plates of the capacitor are then connected to an ideal inductor of inductance $L$. The current through the inductor when the potential difference across the capacitor reduces to $V_2$ is

Similar Questions

The switch is in position $A$ for a long time. At time $t=0$,it is shifted to position $B$. Find the maximum charge that will accumulate on the capacitor.

For which two reasons is the discussion of $LC$ oscillations not realistic?

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:

If $C$ and $L$ denote capacitance and inductance respectively,then the dimensions of $LC$ are

$A$ fully charged capacitor $C$ with initial charge $q_0$ is connected to a coil of self-inductance $L$ at $t = 0$. The time at which the energy is stored equally between the electric and the magnetic fields is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module