Two identical capacitors have same capacitance C. One of them is charged to the potential V and other to the potential 2V. The negative ends of both are connected together. When the positive ends are also joined together, the decrease in energy of the com

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Solution

Q.
Two identical capacitors have same capacitance C. One of them is charged to the potential V and other to the 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 [2024].

1 $\frac{1}{4} C V^{2}$

2 $2 C V^{2}$

3 $\frac{1}{2} C V^{2}$

4 $\frac{3}{4} C V^{2}$

Ans.
(1)

Initial energy $= \frac{1}{2} C V^{2} + \frac{1}{2} C \times 4 V^{2} = \frac{5 C V^{2}}{2}$

$\frac{2 C V - q}{C} = \frac{C V + q}{C}$

$2 C V - C V = 2 q$

$q = \frac{C V}{2}$

Final charge on capacitor $= \frac{3 C V}{2}$

$E n e r g y_{final} = 2 \times {(\frac{3 C V}{2})}^{2} \times \frac{1}{2 C} = \frac{9 C V^{2}}{4}$

Decrease in Energy $= \frac{5 C V^{2}}{2} - \frac{9 C V^{2}}{4} = \frac{C V^{2}}{4}$

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