Two metallic spheres of radii $1\mathrm{cm}$ and $3\mathrm{cm}$ are given charges of $-1\times {10}^{-2}\mathrm{C}$ and $5\times {10}^{-2}\mathrm{C}$respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is:

Three capacitors, each of capacitance $C$ and of breakdown voltage $V$ are joined in series. The capacitance and breakdown voltage of the combination will be 

A parallel plate  capacitor has uniform electric field  $E$ in the space between the plates.If the distance between the plates is $d$ and area of each plate is  $A$, the energy stored in the capacitor is ;

Two thin dielectric slabs of dielectric constants $K_1$ and $K_2\left({ K}_1<K_2\right)$ are inserted between plates of a parallel plate capacitor, as shown in the figure. The variation of electric field $\text{'}E\text{'}$ between the plates with distance $\text{'}d\text{'}$ as measured from plate $P$ is correctly shown by:

A parallel plate air capacitor of capacitance $C$ is connected to a cell of emf $V$ and then disconnected from it. A dielectric slab of dielectric constant $K$, which can just fill the air gap of the capacitor, is now inserted in it. Which of the following is incorrect? 

A capacitor of $2\mu F$ is charged as shown in the diagram. When the switch $S$ is turned to position $2 ,$ the percentage of its stored energy dissipated is :

A parallel- plate capacitor of area $\mathrm{A},$plate separation $\mathrm{d}$ and capacitance $\mathrm{C}$ is filled with four dielectric materials having dielectric constant ${\mathrm{k}}_1, {\mathrm{k}}_2, {\mathrm{k}}_3$ and ${\mathrm{k}}_4$ as shown in the figure below. If a single dielectric material is to be used to have the same capacitance $\mathrm{C}$ in this capacitor, then its dielectric constant $\mathrm{k}$ is given by