A body of capacity $4\,\mu \,F$ is charged to $80\,V$ and another body of capacity $6\,\mu \,F$ is charged to $30\,V$. When they are connected the energy lost by $4\,\mu \,F$ capacitor is.......$mJ$

A $40$ $\mu F$ capacitor in a defibrillator is charged to $3000\,V$. The energy stored in the capacitor is sent through the patient during a pulse of duration $2\,ms$. The power delivered to the patient is......$kW$

Consider a simple $RC$ circuit as shown in Figure $1$.

Process $1$: In the circuit the switch $S$ is closed at $t=0$ and the capacitor is fully charged to voltage $V_0$ (i.e. charging continues for time $T \gg R C$ ). In the process some dissipation ( $E_D$ ) occurs across the resistance $R$. The amount of energy finally stored in the fully charged capacitor is $EC$.

Process $2$: In a different process the voltage is first set to $\frac{V_0}{3}$ and maintained for a charging time $T \gg R C$. Then the voltage is raised to $\frac{2 \mathrm{~V}_0}{3}$ without discharging the capacitor and again maintained for time $\mathrm{T} \gg \mathrm{RC}$. The process is repeated one more time by raising the voltage to $V_0$ and the capacitor is charged to the same final

take $\mathrm{V}_0$ as voltage

These two processes are depicted in Figure $2$.

 ($1$) In Process $1$, the energy stored in the capacitor $E_C$ and heat dissipated across resistance $E_D$ are released by:

$[A]$ $E_C=E_D$ $[B]$ $E_C=E_D \ln 2$ $[C]$ $\mathrm{E}_{\mathrm{C}}=\frac{1}{2} \mathrm{E}_{\mathrm{D}}$ $[D]$ $E_C=2 E_D$

 ($2$) In Process $2$, total energy dissipated across the resistance $E_D$ is:

$[A]$ $\mathrm{E}_{\mathrm{D}}=\frac{1}{2} \mathrm{CV}_0^2$     $[B]$ $\mathrm{E}_{\mathrm{D}}=3\left(\frac{1}{2} \mathrm{CV}_0^2\right)$    $[C]$ $\mathrm{E}_{\mathrm{D}}=\frac{1}{3}\left(\frac{1}{2} \mathrm{CV}_0^2\right)$   $[D]$ $\mathrm{E}_{\mathrm{D}}=3 \mathrm{CV}_0^2$

Given the answer quetion  ($1$) and  ($2$)

A $400\, pF$ capacitor is charged with a $100\, V$ battery. After disconnecting battery this capacitor is connected with another $400\, pF$ capacitor. Then find out energy loss.

A capacitor $4\,\mu F$ charged to $50\, V$ is connected to another capacitor of $2\,\mu F$ charged to $100 \,V$ with plates of like charges connected together. The total energy before and after connection in multiples of $({10^{ - 2}}\,J)$ is

A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to the electromotive force of the battery. The ratio of the energy stored in the capacitor and the work done by the battery will be