A parallel-plate capacitor contains a mica sheet of thickness ${10}^{-3} \mathrm{m}$ and a sheet of fibre of thickness $0.5\times {10}^{-3} \mathrm{m}$. The dielectric constant of mica is 8 and that of fibre is $2.5.$Assuming that the fibre breaks down when subjected to an electric field of $6.4\times {10}^6 \mathrm{V}/\mathrm{m}$ find the maximum safe voltage that can be applied to the capacitor. 

Find the equivalent capacitance of the system of capacitors between the two points $A$ and $B$, Fig. $4.87.$

A parallel-plate capacitor with a plate separation of  $d_1=1\mathrm{cm}$ has $29\mathrm{kV}$ applied across the plates. Show why the air breaks down when a thin piece of glass $(K=6.5)$ with a dielectric strength of $290\mathrm{kV}/\mathrm{cm}$ and thickness $d_2=0.20 \mathrm{cm}$ is inserted as shown in figure. An air has a dielectric strength of $30\mathrm{kV}/\mathrm{cm}.$

 One plate of a capacitor is fixed and the other plate is connected to a spring, other end of which is attached to a right wall Fig. The plate area of the capacitor is $A$ and the separation between the plates is $d$. When the switch $S$ is closed, the distance between the plates is $d$. When the switch $S$ is closed, the distance between the plates reduces to a steady value $0.8 d$. Find the force constant $k$ of the spring.

A parallel plate capacitor has three different dielectric materials as shown in Fig. Find the equivalent capacitance across the two plates, $P_1$ and $P_2$.

In Fig, we see a system of capacitors joined to a cell of emf $12$ Volts. Find the charge on the capacitor $C_1$ when

Both the two keys $K_1$ and $K_2$ are closed.

In Fig. , we see many capacitors joined to a cell of emf $12$ volts. Find the charge on the capacitor $C_1$ 

when only ${\mathrm{K}}_1$ is closed.