Two capacitors each of $1\,\mu F$ capacitance are connected in parallel and are then charged by a $200\,V$ $d.c.$ supply. The total energy of their charges (in $joules$) is

In the circuit shown in the figure,the charge stored in the capacitor of capacity $5 \ \mu F$ is......$ \mu C$.

Following operations can be performed on a capacitor: $X$ - connect the capacitor to a battery of $emf$ $E$. $Y$ - disconnect the battery. $Z$ - reconnect the battery with polarity reversed. $W$ - insert a dielectric slab of dielectric constant $K$ in the capacitor. Which of the following statements is correct?

Consider an evacuated cylindrical chamber of height $h$ having rigid conducting plates at the ends and an insulating curved surface as shown in the figure. $A$ number of spherical balls made of a light weight and soft material and coated with a conducting material are placed on the bottom plate. The balls have a radius $r \ll h$. Now a high voltage source $(HV)$ is connected across the conducting plates such that the bottom plate is at $+V_0$ and the top plate at $-V_0$. Due to their conducting surface,the balls will get charged,will become equipotential with the plate and are repelled by it. The balls will eventually collide with the top plate,where the coefficient of restitution can be taken to be zero due to the soft nature of the material of the balls. The electric field in the chamber can be considered to be that of a parallel plate capacitor. Assume that there are no collisions between the balls and the interaction between them is negligible. (Ignore gravity)
$(1)$ Which one of the following statements is correct?
$(A)$ The balls will stick to the top plate and remain there
$(B)$ The balls will bounce back to the bottom plate carrying the same charge they went up with
$(C)$ The balls will bounce back to the bottom plate carrying the opposite charge they went up with
$(D)$ The balls will execute simple harmonic motion between the two plates
$(2)$ The average current in the steady state registered by the ammeter in the circuit will be
$(A)$ zero
$(B)$ proportional to the potential $V_0$
$(C)$ proportional to $V_0^{1/2}$
$(D)$ proportional to $V_0^2$

In the electrical circuit shown below,the amount of charge stored in the capacitor is . . . . . . $\mu C$.

The switch $S_w$ is shifted from position $1$ to position $2$ as shown in the figure. Heat generated in the circuit is