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

In the circuit shown in the figure, the energy stored in \(6~\mu\text{F}\) capacitor will be:
      

The dimension of (1/2) ${\epsilon }_0{E}^2<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>({\epsilon }_0$: permittivity of free space; E: electric field) is

(1) MLT^–1

(2) ML²L^–2

(3) ML^–1T^–2

(4) ML²T^–1

The capacity of a condenser is 4 × 10^–6 farad and its potential is 100 volts. The energy released on discharging it fully will be -

1. 0.02 Joule

2. 0.04 Joule

3. 0.025 Joule

4. 0.05 Joule

The energy stored in a condenser of capacity C which has been raised to a potential V is given by -

1. $\frac{1}{2}CV$

2. $\frac{1}{2}C{V}^2$

3. CV

4. $\frac{1}{2VC}$