In the circuit below,$C_1 = 20 \, \mu F$,$C_2 = 40 \, \mu F$,and $C_3 = 50 \, \mu F$. If no capacitor can sustain more than $50 \, V$,then the maximum potential difference between $X$ and $Y$ is .......... $V$.

Two positrons $(e^+)$ and two protons $(p)$ are kept on four corners of a square of side $a$ as shown in the figure. The mass of a proton is much larger than the mass of a positron. Let $q$ denote the charge on the proton as well as the positron. Then,the kinetic energies of one of the positrons and one of the protons,respectively,after a very long time will be:

In the following diagram,the charge and potential difference across $8\, \mu F$ capacitance will be respectively

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 $T \gg RC$). In the process,some dissipation $(E_D)$ occurs across the resistance $R$. The amount of energy finally stored in the fully charged capacitor is $E_C$.
Process $2$: In a different process,the voltage is first set to $V_0/3$ and maintained for a charging time $T \gg RC$. Then the voltage is raised to $2V_0/3$ without discharging the capacitor and again maintained for time $T \gg RC$. The process is repeated one more time by raising the voltage to $V_0$ and the capacitor is charged to the same final voltage $V_0$.
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 related by:
$[A]$ $E_C = E_D$
$[B]$ $E_C = E_D \ln 2$
$[C]$ $E_C = \frac{1}{2} E_D$
$[D]$ $E_C = 2 E_D$
$(2)$ In Process $2$,the total energy dissipated across the resistance $E_D$ is:
$[A]$ $E_D = \frac{1}{2} CV_0^2$
$[B]$ $E_D = 3 \left( \frac{1}{2} CV_0^2 \right)$
$[C]$ $E_D = \frac{1}{3} \left( \frac{1}{2} CV_0^2 \right)$
$[D]$ $E_D = 3 CV_0^2$
Select the correct pair of answers for $(1)$ and $(2)$.

Three point charges $1 \ C$,$-2 \ C$,and $-2 \ C$ are placed at the vertices of an equilateral triangle of side $1 \ m$. The work done by an external force to increase the separation of the charges to $2 \ m$ in joules is ($\varepsilon_0 =$ permittivity of air).

Two capacitors $C_1 = 2\,\mu F$ and $C_2 = 6\,\mu F$ in series are connected in parallel to a third capacitor $C_3 = 4\,\mu F$. This arrangement is then connected to a battery of $e.m.f. = 2\,V$,as shown in the figure. How much energy is lost by the battery in charging the capacitors?