A metallic sphere of capacitance $C_1$, charged to electric potential $V_1$ is connected by a metal wire to another metallic sphere of capacitance $C_2$ charged to electric potential $V_2$. The amount of heat produced in connecting the wire during the process is:

1.$\frac{C_1{C}_2}{2\left(C_1+C_2\right)}{\left(V_1+V_2\right)}^2$

2. $\frac{C_1{C}_2}{2(C_1+C_2)}{(V_1-V_2)}^2$

3. $\frac{C_1{C}_2}{C_1+C_2}{(V_1-V_2)}^2$

4. zero

Four equal charges Q are placed at the four corners of a square of each side is ‘a’. Work done in removing a charge – Q from its centre to infinity is 

(1) 0

(2) $\frac{\sqrt{2}{Q}^2}{4\pi {\epsilon }_{0}a}$

(3) $\frac{\sqrt{2}{Q}^2}{\pi {\epsilon }_{0}a}$

(4) $\frac{Q^2}{2\pi {\epsilon }_{0}a}$

Two spheres of radius a and b respectively are charged and joined by a wire. The ratio of the electric field at the surface of the spheres is 

(1) a/b

(2) b/a

(3) a²/b²

(4) b²/a²

An electron of mass m and charge e is accelerated from rest through a potential difference V in vacuum. The final speed of the electron will be 

(1) $V\sqrt{e/m}$

(2) $\sqrt{eV/m}$

(3) $\sqrt{2eV/m}$

(4) $2eV/m$

A capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of the resulting system 

1. increases by a factor of 4

2.decreases by a factor of 2

3. remain the same 

4. increases by a factor of 2

The diagrams below show regions of equipotentials.

A parallel-plate capacitor of area A, plate separation d, and capacitance C is filled with four dielectric materials having dielectric constants $k_1,k_2,k_3$ $$and $k_4$ as shown in the figure below. If a single dielectric material is to be used to have the same capacitance C in this capacitor, then its dielectric constant k is given by

1. $\mathrm{k}={\mathrm{k}}_1+{\mathrm{k}}_2+{\mathrm{k}}_3+3{\mathrm{k}}_4$

2. $k=\frac{2}{3}\left(k_1+k_2+k_3\right)+2k_4$

3. $\frac{1}{k}=\frac{3}{2\left(k_1+k_2+k_3\right)}+\frac{1}{2k_4}$

4. $\frac{1}{\mathrm{k}}=\frac{1}{{\mathrm{k}}_1}+\frac{1}{{\mathrm{k}}_2}+\frac{1}{{\mathrm{k}}_3}+\frac{3}{2{\mathrm{k}}_4}$

A capacitor of \(2~\mu\text{F}\) is charged as shown in the figure. When the switch \(S\) is turned to position \(2\), the percentage of its stored energy dissipated is: