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JEE Main 2024 (30 Jan, Shift 1) · Charge Sharing & Loss of Energy

Charge Sharing & Loss of Energy question from JEE Main 2024 (30 Jan, Shift 1)

Q10JEE Main 2024 · 30 JAN · SHIFT 1Medium

Charge Sharing & Loss of Energy

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 $\frac{x}{3}E$ , where $x$ is _______.

Numerical answer type. Work it out, then open the answer.

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Answer: 2

Loss on joining like plates: $\Delta U = \frac{1}{2}\frac{C_1C_2}{C_1 + C_2}(V_1 - V_2)^2$
$\Delta U = \frac{1}{2} \cdot \frac{2C}{3} \cdot V^2 = \frac{1}{3}CV^2$
With $E = \frac{1}{2}CV^2$ : $\Delta U = \frac{2}{3}E$
So $x = 2$ .

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