A capacitor of capacity 'C' is charged to a p | vedclass

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

Question

(C) The total energy in an $LC$ circuit is conserved.Initially,the energy stored in the capacitor is $U_i = \frac{1}{2}CV_1^2$.When the potential diff

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) The total energy in an $LC$ circuit is conserved.Initially,the energy stored in the capacitor is $U_i = \frac{1}{2}CV_1^2$.When the potential difference across the capacitor becomes $V_2$,the energy stored in the capacitor is $U_c = \frac{1}{2}CV_2^2$.The energy stored in the inductor at this instant is $U_L = \frac{1}{2}LI^2$.By the law of conservation of energy: $U_i = U_c + U_L$.$\frac{1}{2}CV_1^2 = \frac{1}{2}CV_2^2 + \frac{1}{2}LI^2$.$LI^2 = C(V_1^2 - V_2^2)$.$I^2 = \frac{C}{L}(V_1^2 - V_2^2)$.$I = \sqrt{\frac{C}{L}(V_1^2 - V_2^2)}$.Thus,the correct option is $C$.

$A$ 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

$A$ $1 \mu F$ capacitor is charged to $50 \ V$ and is then discharged through a $10 \ mH$ inductor of negligible resistance. The maximum current in the inductor is (in $A$)

$A$ $LC$ circuit is in the state of resonance. If $C = 0.1 \mu F$ and $L = 0.25 \ H$. Neglecting the ohmic resistance of the circuit,what is the frequency of oscillations in $Hz$?

$A$ 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:

The frequency of oscillation of the current in the given circuit is:

An oscillator circuit consists of an inductance of $0.5 \ mH$ and a capacitor of $20 \ \mu F$. The resonant frequency of the circuit is nearly......$Hz$

Vedclass Test Series

Exam Paper Generator

Online Exam Module