Q 12-02-079JEE MainJEE Main 2024 (30 Jan, Shift 1)Medium
A capacitor of capacitance $C$ and potential $V$ has energy $E$. It is connected to another capacitor of capacitance $2C$ and potential $2V$. Then the loss of energy is $\dfrac x3E$, where $x$ is ______.
Numerical value type. Enter your answer.
Answer: 2
With $E = \tfrac12CV^2$, the energy lost on joining (like plates together) is
$$\Delta U = \frac{C_1C_2}{2(C_1 + C_2)}(V_1 - V_2)^2 = \frac{C\cdot2C}{2\cdot3C}V^2 = \frac{CV^2}{3} = \frac23E$$
So $x = 2$.
Solution by Sreeraj P, M.Sc Physics