Q. 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) $\frac{C_{1}V_{1} + C_{2}V_{2}}{C_{1} + C_{2}}$
Explanation

(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 =$\frac{net\ charge}{total\ capacity}$
$ie\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ V = \ \frac{q_{1} + q_{2}}{C_{1} + C_{2}}$
or $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ V\ = \ \frac{C_{1}V_{1} + C_{2}V_{2}}{C_{1} + C_{2}}$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.