Capacitors: Practice Problem & Solution
Two metallic spheres of radii $1 \text{ cm}$ and $2 \text{ cm}$ are given charges $10^{-2} \text{ C}$ and $5 \times 10^{-2} \text{ C}$ respectively. If they are connected by a conducting wire, the final charge on the smaller sphere is (1995)
Solution Explained:
To solve this problem, we apply the core principles of Capacitors. Understanding the underlying formula is key to arriving at the correct answer below:
Total charge $Q = 10^{-2} + 5 \times 10^{-2} = 6 \times 10^{-2} \text{ C}$. Capacitances are proportional to radii, so $C_1 : C_2 = 1 : 2$. Charge on the smaller sphere is $q_1 = Q \times \frac{C_1}{C_1 + C_2} = 6 \times 10^{-2} \times \frac{1}{3} = 2 \times 10^{-2} \text{ C}$.
Leave a Reply