(a) "There is a limit to the amount of charge that can be stored on a given capacitor." Explain. (b) A capacitor is charged by a battery to a…

When a conductor holds a large amount of charge its potential is also high. If the electric field becomes high enough, the atoms or molecules of the surrounding medium get ionized. A breakdown occurs in the medium and the charge on the conductor gets neutralized or leaks away.

The common potential after the connection of two capacitors:

Given $\displaystyle V_{1}=V$, $\displaystyle V_{2}=0$; $\displaystyle C_{1}=C_{2}=C$

$\displaystyle V^{\prime}=\frac{C V}{2 C}=\frac{V}{2}$

$\displaystyle U_{i}=\frac{1}{2} C V^{2}$

$\displaystyle U_{f}=\frac{1}{2} C^{\prime} V^{\prime 2}$

$\displaystyle =\frac{1}{2} \times 2 C \times\left(\frac{V}{2}\right)^{2}$

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

$\displaystyle \frac{U_{f}}{U_{i}}=\frac{1}{2}$