Question

A capacitor of capacitance $900\, \mu F$ is charged by a $100\, V$ battery The capacitor is disconnected from the battery and connected to another uncharged identical capacitor such that one plate of uncharged capacitor connected to positive plate and another plate of uncharged capacitor connected to negative plate of the charged capacitor The loss of energy in this process is measured as $x \times 10^{-2} J$ The value of $x$ is ______

Answer 1

The correct answer is 225.

Common potential will be developed across both capacitors by kVL
Total charge on left plates of capacitors should be conserved.
∴90mc+0=2cv0​
cv0​=45mc

Heat dissipated =Ui​−Uf​ [Change in energy stored in the capacitors]
=21​900μF(90mc)2​−2×21​900μF(45mc)2​[U=2cQ2​]
=2×900×10−61​(8100−4050)×10−6
=2.25 Joule
OR
Heat =21​C1​+C2​C1​C2​​(V1​−V2​)2
=21​2CC2​(100−0)2
=21​2900×10−6​×104=49​ Joule =2.25 Joule