A slab of material of dielectric constant $k$ has the same area as the plates of a parallel plate capacitor but has a thickness $\left(\frac{3}{4}\right)d$, where $d$ is the separation of the plates. The ratio of the capacitance $C$ (in the presence of the dielectric) to the capacitance $C_0$ (in the absence of the dielectric) is

In the given circuit diagram when the current. reaches steady state in the circuit, the charge on the capacitor of capacitance $C$ will be

A network of four capacitors of capacities equal to $C_1=C, C_2=2C, C_3=3C$ and $C_4=4C$ are connected to a battery as shown in the figure. The ratio of the charge on $C_2$ and $C_4$ is

Consider the situation shown in the figure. The capacitor $A$ has a charge $q$ on it whereas $B$ is uncharged. The charge appearing on the capacitor $B$ a long time after the switch is closed is 

A capacitance of $2 \mu \mathrm{F}$ is required in an electrical circuit across a potential difference of $1.0 \mathrm{kV}$. A large number of $1 \mathrm{\mu F}$capacitors are available which can withstand a potential difference of not more than $300 \mathrm{V}$.The minimum number of capacitors required to achieve this is 

The electric field due to a uniformly charged sphere of radius $R$ as a function of the distance from its centre is represented graphically by

Energy stored in a condenser of capacity $10 \mu \mathrm{F}$, charged to $6\mathrm{kV}$ is used to lift a mass of $10 \mathrm{gm}$. The height to which the body can be raised is (Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$) 

A thunder cloud and the earth's surface may be regarded as a pair of charged parallel plates separated by a distance $h$ and the capacitance of the system is $C$. When a flash of mean current $i$ occurs for a time duration $t$, the electric field strength between the cloud and earth is reduced by

A combination of capacitors is set up as shown in the figure. The magnitude of the electric field, due to a point charge $Q$ (having a charge equal to the sum of the charges on the $4 \mu \mathrm{F}$ and $9 \mu \mathrm{F}$ capacitors), at a point distance $30 \mathrm{m}$ from it, would equal