A condenser of capacity C_1 is charged to a p | vedclass

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

Question

(A) The initial energy stored in the capacitor $C_1$ is $U_0 = \frac{1}{2} C_1 V_0^2$.When connected in parallel to an uncharged capacitor $C_2$,the c

Vedclass · Accepted Answer

$\frac{C_2}{C_1 + C_2} U_0$

Vedclass · Answer

(A) The initial energy stored in the capacitor $C_1$ is $U_0 = \frac{1}{2} C_1 V_0^2$.When connected in parallel to an uncharged capacitor $C_2$,the charge redistributes until both capacitors reach a common potential $V = \frac{C_1 V_0}{C_1 + C_2}$.The final energy stored in the system is $U_f = \frac{1}{2} (C_1 + C_2) V^2 = \frac{1}{2} (C_1 + C_2) \left( \frac{C_1 V_0}{C_1 + C_2} \right)^2 = \frac{C_1^2 V_0^2}{2(C_1 + C_2)}$.The energy dissipated (loss of energy) is $\Delta U = U_0 - U_f$.$\Delta U = \frac{1}{2} C_1 V_0^2 - \frac{C_1^2 V_0^2}{2(C_1 + C_2)} = \frac{C_1 V_0^2}{2} \left( 1 - \frac{C_1}{C_1 + C_2} \right) = \frac{C_1 V_0^2}{2} \left( \frac{C_2}{C_1 + C_2} \right)$.Since $U_0 = \frac{1}{2} C_1 V_0^2$,we substitute this into the expression:$\Delta U = \frac{C_2}{C_1 + C_2} U_0$.

$A$ condenser of capacity $C_1$ is charged to a potential $V_0$. The electrostatic energy stored in it is $U_0$. It is connected to another uncharged condenser of capacity $C_2$ in parallel. The energy dissipated in the process is

Similar Questions

Two metal spheres of radii $0.01 \ m$ and $0.02 \ m$ are given a charge of $15 \ mC$ and $45 \ mC$ respectively. They are then connected by a wire. The final charge on the first sphere is $\ldots \ldots \ldots \times 10^{-3} \ C$.

Two capacitors of $1\,\mu F$ and $2\,\mu F$ are charged to $1200\,V$. If they are connected in parallel such that the positive plate of one is connected to the negative plate of the other,what will be the new charge on each capacitor?

Two metallic spheres of radii $1 \, cm$ and $3 \, cm$ are given,with charges of $-1 \times 10^{-2} \, C$ and $5 \times 10^{-2} \, C$ respectively. If these are connected by a conducting wire,the final charge on the bigger sphere is

Vedclass Test Series

Exam Paper Generator

Online Exam Module