A dielectric slab of dielectric constant $K$ is placed between the plates of a parallel plate capacitor carrying charge $q.$ The induced charge $q^{\text{'}}$ on the surface of slab is given by

Two charged capacitors have their outer plates fixed and inner plates connected by a spring of force constant $\text{'}\mathrm{k}\text{'}.$ The charge on each capacitor is $\mathrm{q}.$ Find the extension in the spring at equilibrium

The following arrangement consists of five identical metal plates parallel to each other. Area of each plate is $\mathrm{A}$ and separation between the successive plates is $\mathrm{d}$. The capacitance between $\mathrm{P}$ and $\mathrm{Q}$ is

A capacitor is half filled with a dielectric $(\mathrm{K}=2)$ as shown in figure $\mathrm{A}$. If the same capacitor is to be filled with same dielectric as shown, what would be the thickness of dielectric so that capacitor still has same capacity?

Capacitors ${\mathrm{C}}_1\left(10\mathrm{\mu F}\right)$ and $C_2\left(20\mu \mathrm{F}\right)$ are connected in series across a $3 \mathrm{kV}$ supply, as shown. What is the charge on the capacitor ${\mathrm{C}}_1$ ?

The charge on the $6 \mathrm{\mu F}$ capacitor in the circuit shown is

In the circuit below ${\mathrm{C}}_1=20 \mathrm{\mu F}, {\mathrm{C}}_2=40 \mathrm{\mu F}$ and ${\mathrm{C}}_3=50 \mathrm{\mu F}.$ If no capacitor can sustain more than $50 \mathrm{V},$ then maximum potential difference between $\mathrm{X}$ and $\mathrm{Y}$ is

In the circuit shown below $C_1=10\mu F,C_2=C_3=$ $20\mu F$, and $C_4=40\mu F$. If the charge on $C_1$ is $20\mu C$ then potential difference between $X$ and $Y$ is