Question

a capacitor of 400*10^-6 is charged to a potential 200v . how much energy is stored in the capacitor? how much energy is supplied by the battery

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{Capacitor},\mathrm{C}=400\times {10}^{-6}\mathrm{F} \\ \mathrm{Potential},\mathrm{V}=200\mathrm{V} \\ \mathrm{Electrostatic}\mathrm{energy}\mathrm{stored}\mathrm{in}\mathrm{the}\mathrm{capacitor}\mathrm{is}, \\ {\mathrm{E}}_{\mathrm{C}}=\frac{1}{2}{\mathrm{CV}}^2 \\ {\mathrm{E}}_{\mathrm{C}}=\frac{1}{2}\times 400\times {10}^{-6}\times {\left(200\right)}^2 \\ {\mathrm{E}}_{\mathrm{C}}=8\mathrm{J} \\ \mathrm{Energy}\mathrm{supplied}\mathrm{by}\mathrm{the}\mathrm{battery}\mathrm{is}, \\ {\mathrm{E}}_{\mathrm{b}}=\mathrm{QV} \\ {\mathrm{E}}_{\mathrm{b}}={\mathrm{CV}}^2.....................\left[\mathrm{because}\mathrm{Q}=\mathrm{C}\times \mathrm{V}\right] \\ {\mathrm{E}}_{\mathrm{b}}=400\times {10}^{-6}\times {\left(200\right)}^2 \\ {\mathrm{E}}_{\mathrm{b}}=16\mathrm{J} \end{gathered}$$