Capacitance Question 1
Question 1 - 2024 (01 Feb Shift 1)
Two identical capacitors have same capacitance C. One of them is charged to the potential V and other to the potential $2 \mathrm{~V}$. 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 :
(1) $\frac{1}{4} \mathrm{CV}^{2}$
(2) $2 \mathrm{CV}^{2}$
(3) $\frac{1}{2} \mathrm{CV}^{2}$
(4) $\frac{3}{4} \mathrm{CV}^{2}$
Show Answer
Answer: (1)
Solution:
$\mathrm{V}{\mathrm{C}}=\frac{\mathrm{q}{\mathrm{net}}}{\mathrm{C}_{\mathrm{net}}}=\frac{\mathrm{CV}+2 \mathrm{CV}}{2 \mathrm{C}}$
$\mathrm{V}_{\mathrm{C}}=\frac{3 \mathrm{~V}}{2}$
Loss of energy
$$ \begin{aligned} & =\frac{1}{2} \mathrm{CV}^{2}+\frac{1}{2} \mathrm{C}(2 \mathrm{~V})^{2}-\frac{1}{2} 2 \mathrm{C}\left(\frac{3 \mathrm{~V}}{2}\right)^{2} \ & =\left(\frac{\mathrm{CV}^{2}}{4}\right) \end{aligned} $$
