Question

When two conductors of charges and potentials $C_{1}, V_{1}$ and $C_{2}, V_{2}$ respectively are joined, the common potential will be :

• A. $\frac{C_{1} V_{1}+C_{2} V_{2}}{V_{1}+V_{2}}$
• B. $\frac{C_{1} V_{1}^{2}+C_{2} V_{2}^{2}}{V_{1}^{2}+V_{2}^{2}}$
• C. $C_{1}+C_{2}$
• D. $\frac{C_{1} V_{1}+C_{2} V_{2}}{C_{1}+C_{2}}$

Answer 1

Answer: (D)

When two conductors of capacities $C_{1}$ and $C_{2}$ and potentials $V_{1}$ and $V_{2}$ are connected by a conducting wire, charge redistributes in these conductors till potential of both the conductors become equal, known as common potential.
Common potential $=\frac{\text { net charge }}{\text { total capacity }}$
i.e, $V =\frac{q_{1}+q_{2}}{C_{1}+C_{2}}$
or $V=\frac{C_{1} V_{1}+C_{2} V_{2}}{C_{1}+C_{2}}$