Three capacitors of capacitances $25 \mu F, 30 \mu F$ and $45 \mu F$ are connected in parallel to a supply of $100 \ V$. Energy stored in the above combination is $E$. When these capacitors are connected in series to the same supply,the stored energy is $\frac{9}{x} E$. The value of $x$ is . . . . . . .

$A$ parallel plate capacitor with a dielectric of dielectric constant $K$ between the plates has a capacitance $C$ and is charged to a potential $V \ volt$. The dielectric slab is slowly removed from between the plates and then reinserted. The net work done by the system in this process is

An automobile spring extends by $0.2\ m$ for a load of $5000\ N$. What is the ratio of the potential energy stored in the spring when it is compressed by $0.2\ m$ to the potential energy stored in a $10\ \mu F$ capacitor at a potential difference of $10000\ V$?

As shown in the figure,the work done in moving a charge $q$ from $A$ to $B$ and from $B$ to $C$ is $2 \ J$ and $-3 \ J$ respectively. The work done in moving the charge from $C$ to $A$ will be ...... $J$.

There exists a uniform electric field $E = 4 \times 10^5 \, Vm^{-1}$ directed along the negative $x$-axis such that the electric potential at the origin is zero. $A$ charge of $-200 \, \mu C$ is placed at the origin,and a charge of $+200 \, \mu C$ is placed at $(3 \, m, 0)$. The electrostatic potential energy of the system is ........... $J$.

For the given circuit,find the potential at point $a$. (in $V$)