Sixty-four conducting drops,each of radius $0.02 \ m$ and each carrying a charge of $5 \ \mu C$,are combined to form a bigger drop. The ratio of the surface charge density of the bigger drop to that of the smaller drop will be ............

In the given figure,the capacitors $C_1, C_3, C_4, C_5$ have a capacitance of $4\,\mu F$ each. If the capacitor $C_2$ has a capacitance of $10\,\mu F$,then the effective capacitance between $A$ and $B$ will be.....$\mu F$.

Each plate of a parallel plate capacitor has a charge $q$ on it. The capacitor is now connected to a battery. Now,

$A$ capacitor $A$ has a capacitance of $15\ \mu F$ when filled with a dielectric of constant $K = 15$. Another capacitor $B$ is air-filled and has a capacitance of $1\ \mu F$. Both are charged to $100\ V$. After charging, the dielectric is removed from capacitor $A$, and the two capacitors are connected in parallel. The common potential difference across them will be ... $V$.

When a potential difference of $10^{3} \, V$ is applied between $A$ and $B$, a charge of $0.75 \, mC$ is stored in the circuit. The value of $C$ is (in $\mu F$):

See the diagram. The area of each plate is $2.0 \,m^{2}$ and $d=2 \times 10^{-3} \,m$. $A$ charge of $8.85 \times 10^{-8} \,C$ is given to plate $Q$. Then the potential of $Q$ becomes (in $\,V$)