A 5   μF capacitor is charged fully by a 220   V supply. It is then disconnected from the…

${\mathrm{C}}_1=5\mu \mathrm{F} {\mathrm{V}}_1=220\mathrm{Volt}$

${\mathrm{C}}_2=2.5\mu \mathrm{F} {\mathrm{V}}_2=0$

Heat loss;

$\Delta \mathrm{H}={\mathrm{U}}_1-{\mathrm{U}}_{\mathrm{t}}=\frac{1}{2}\frac{{\mathrm{C}}_1{\mathrm{C}}_2}{{\mathrm{C}}_1+{\mathrm{C}}_2}{\left({\mathrm{v}}_1-{\mathrm{v}}_2\right)}^2$

$=\frac{1}{2}\times \frac{5\times 2.5}{(5+2.5)}(220-0{)}^2\mu \mathrm{J}$

$=\frac{5}{2\times 3}\times 22\times 22\times 100\times {10}^{-6}\mathrm{J}$

$=\frac{5\times 11\times 22}{3}\times {10}^{-4}\mathrm{J}=\frac{55\times 22}{3}\times {10}^{-4}\mathrm{J}$

$=\frac{1210}{3}\times {10}^{-4}\mathrm{J}=\frac{1210}{3}\times {10}^{-3}\mathrm{J}=4\times {10}^{-2}$

According to questions

$\frac{x}{100}=4\times {10}^{-2}$

so, $x=4$