Q 12-02-063JEE MainJEE Main 2024 (1 Feb, Shift 1)Medium
Two identical capacitors have the same capacitance $C$. One of them is charged to potential $V$ and the other to potential $2V$. The negative ends of both are connected together. When the positive ends are also joined together, the decrease in energy of the combined system is
Answer: (A) $\dfrac{1}{4}CV^2$
Initial energy: $U_i = \frac12CV^2 + \frac12C(2V)^2 = \frac52CV^2$.
Common potential: $V_c = \dfrac{CV + 2CV}{2C} = \dfrac{3V}{2}$.
Final energy: $U_f = \frac12(2C)\left(\frac{3V}{2}\right)^2 = \frac94CV^2$.
$$\Delta U = \frac52CV^2 - \frac94CV^2 = \frac14CV^2$$
Solution by Sreeraj P, M.Sc Physics