When a parallel plate capacitor is connected to a source of constant potential difference,

Statement $(A)$: Inside a charged hollow metal sphere,$E = 0$ and $V \neq 0$. ($E$ = electric field,$V$ = electric potential).
Statement $(B)$: The work done in moving a positive charge on an equipotential surface is zero.
Statement $(C)$: When two like charges are brought closer,their mutual electrostatic potential energy will increase.

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 .......... $V$.

Four capacitors with capacitances $C_1 = 1\,\mu F, C_2 = 1.5\,\mu F, C_3 = 2.5\,\mu F$ and $C_4 = 0.5\,\mu F$ are connected as shown and are connected to a $30\,V$ source. The potential difference between points $a$ and $b$ is.....$V$.

Two capacitors,one of capacitance $C$ and the other of capacitance $C/2$,are connected in parallel to a battery of potential difference $V$. Calculate the heat produced in the connecting wires.

Identify the correct statements:
$A$. Effective capacitance of a series combination of capacitors is always smaller than the smallest capacitance of the capacitor in the combination.
$B$. When a dielectric medium is placed between the charged plates of a capacitor,displacement of charges cannot occur due to the insulation property of the dielectric.
$C$. Increasing the area of the capacitor plate or decreasing the thickness of the dielectric is an alternate method to increase the capacitance.
$D$. For a point charge,concentric spherical shells centered at the location of the charge are equipotential surfaces.
Choose the correct answer from the options given below.