Concepts Of Physics MCQ Edition [Volume 2]PhysicsCapacitors
An assembly comprises three conducting concentric spherical shells having radii a , b , and c , as shown in the figure. Determine the capacitance of the assembly between points A and B .
Options
- A4 ₀ (a^2 + c^2) b
- B4 ₀ (a b + b c) c - a
- C4 ₀ a c a + c
- D4 ₀ a c c - a
Correct answer
D. 4 ₀ a c c - a
Step-by-step solution
The given assembly can be considered as two spherical capacitors connected in series because the middle shell is isolated and uncharged. The first capacitor C₁ is formed by the inner shell of radius a and the middle shell of radius b . Its capacitance is: C₁ = 4 ₀ a b b - a The second capacitor C₂ is formed by the middle shell of radius b and the outer shell of radius c . Its capacitance is: C₂ = 4 ₀ b c c - b The equivalent capacitance C_ eq for the series combination is given by: 1 C_ eq = 1 C₁ + 1 C₂ Substitutin