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

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(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

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

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(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

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