Three identical charged capacitors each of capacitance $5 \,\mu F$ are connected as shown in the figure. The potential difference across capacitor $(3)$,a long time after the switches $K_1$ and $K_2$ are closed,is ............ $V$.

The capacities and connection of five capacitors are shown in the adjoining figure. The potential difference between the points $A$ and $B$ is $60\;V$. Then the equivalent capacity between $A$ and $B$ and the charge on $5\;\mu F$ capacitor will be respectively:

Two capacitors $C_1 = 2 \mu F$ and $C_2 = 4 \mu F$ are connected in a circuit as shown in the figure. The potential difference $(V_A - V_B)$ is....$V$

The figure shows two identical parallel plate capacitors $A$ and $B$ of capacitances $C$ connected to a battery. The key $K$ is initially closed. The switch is now opened and the free spaces between the plates of the capacitors are filled with a dielectric of dielectric constant $K=3$. Then which of the following statement$(s)$ is/are true?

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 $(2)$.

Find the potentials at points $A$ and $B$ in the circuit shown in the figure.