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?

In the following circuit $C_1=12 \mu F, C_2=C_3=4 \mu F$ and $C_4=C_5=2 \mu F$. The charge stored in $C_3$ is . . . . . $\mu C$.

Four capacitors of capacitance $10\, \mu F$ and a battery of $200\, V$ are arranged as shown. How much charge will flow through $AB$ after the switch $S$ is closed?

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 capacitors are connected as shown in the figure. Then the charge on capacitor $C_1$ is.....$\mu C$.

$A$ series combination of $n_1$ capacitors,each of value $C_1$,is charged by a source of potential difference $6 \ V$. Another parallel combination of $n_2$ capacitors,each of value $C_2$,is charged by a source of potential difference $2 \ V$. The total energy of both combinations is the same. The value of $C_2$ in terms of $C_1$ is: