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 $2 V$. 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) $\frac{1}{4} CV^{2}$
(2) $2 CV^{2}$
(3) $\frac{1}{2} CV^{2}$
(4) $\frac{3}{4} CV^{2}$
Show Answer
Answer: (1)
Solution:
$V _C=\frac{q _{net}}{C _{net}}=\frac{CV+2 CV}{2 C}$
$V _C=\frac{3 V}{2}$
Loss of energy
$$ \begin{aligned} & =\frac{1}{2} CV^{2}+\frac{1}{2} C(2 V)^{2}-\frac{1}{2} 2 C\left(\frac{3 V}{2}\right)^{2} \\ & =\left(\frac{CV^{2}}{4}\right) \end{aligned} $$
