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  4. A capacitor of capacitance C has charge Q. It is connected to an identical capacitor through a resistance. The heat produced in the resistance is

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Q. A capacitor of capacitance $C$ has charge $Q$. It is connected to an identical capacitor through a resistance. The heat produced in the resistance is

Current Electricity

Solution:

As the capacitors are identical, each of them finally have charge $Q / 2$.
Initial energy of the system is $E_{i}=\frac{Q^{2}}{2 C}$
Final energy of the system is $E_{f}=2\left[\frac{(Q / 2)^{2}}{2 C}\right]=\frac{Q^{2}}{4 C}$
Heat produced $=$ loss in energy $=E_{i}-E_{f}=\frac{Q^{2}}{4 C}$