Question

Two insulated charged spheres of radii $R_{1}$ and $R_{2}$ having charges $Q_{1}$ and $Q_{2}$ , respectively, are connected to each other; then there is

• A. no change in the energy of the system
• B. an increase in the energy of the system
• C. always a decrease in the energy of the system
• D. a decrease in energy of the system unless $q_{1}R_{2}=q_{2}R_{1}$

Answer 1

Answer: (D)

Decrease in energy of the system after connection is given by
$\Delta U=\frac{1}{2}\left(\frac{C_{1} C_{2}}{C_{1} + C_{2}}\right)\left(V_{1} - V_{2}\right)^{2}$
$\Delta U=0,$ If $V_{1}=V_{2}$
or $\frac{k q_{1}}{R_{1}}=\frac{k q_{2}}{R_{2}}$
or $q_{1}R_{2}=q_{2}R_{1}$