Question

Two metal spheres of capacitance C₁ and C₂ carry some charges. They are put in contact and then separated. The final charges Q₁ and Q₂ on them will satisfy
(a) $\frac{Q_1}{Q_2}<\frac{C_1}{C_2}$

(b) $\frac{Q_1}{Q_2}=\frac{C_1}{C_2}$

(c) $\frac{Q_1}{Q_2}>\frac{C_1}{C_2}$

(d) $\frac{Q_1}{Q_2}=\frac{C_2}{C_1}$.

Answer 1

(b) $\frac{Q_1}{Q_2}=\frac{C_1}{C_2}$

When the spheres are connected, charges flow between them until they both acquire the same common potential V.
The final charges on the spheres are given by
Q₁ = C_​1V and Q₂ = C₂V

$\therefore \frac{Q_1}{Q_2}=\frac{C_{1}V}{C_{2}V}$ = $\frac{C_1}{C_2}$

C1C2V