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

Two capacitors of capacitance $C$ and $2C$ are connected in parallel and charged to a potential difference $V$. The battery is then disconnected,and the space between the plates of the capacitors is completely filled with a dielectric material of constant $K$. Determine the new potential difference across the capacitors.

As shown in the figure,what will be the charge on each capacitor and the potential difference across each,respectively?

Effective capacitance of parallel combination of two capacitors $C_{1}$ and $C_{2}$ is $10\; \mu F$. When these capacitors are individually connected to a voltage source of $1\; V,$ the energy stored in the capacitor $C_{2}$ is $4$ times that of $C_{1}$. If these capacitors are connected in series,their effective capacitance will be (in $; \mu F$)

$A$ body of mass $1 \,g$ and carrying a charge $10^{-8} \,C$ passes through two points $P$ and $Q$. $P$ and $Q$ are at electric potentials $600 \,V$ and $0 \,V$, respectively. The velocity of the body at $Q$ is $20 \,cm/s$. Its velocity in $m/s$ at $P$ is:

$A$ hollow metal sphere has a radius $r$. The potential difference between a point on its surface and a point at a distance $3r$ from its center is $V$. The electric intensity at the distance $3r$ from the center of the sphere will be