A spherical capacitor has outer sphere of radius (5 ~cm ) and inner sphere of radius (2 ~cm ). When the inner sphere is earthed, its capacity is (C₁ ) and when the outer sphere is earthed its capacity is (C₂ ). Then ( C₁ C₂ ) is

Step-by-step solution

Key Idea If a spherical capacitor has outer radius (R₂ ) and inner radius (R₁ ). Then the capacitance, (a) when outer shell is earthed, (C=4 ₀ R₁ R₂ R₂-R₁ ) (b) When inner shell is earthed, (C^ =C+4 ₀ R₂ ) Given, radius of outer sphere of capacitor, (R₁=2 ~cm ) and Radius of inner sphere of capacitor, (R₂=5 ~cm ) ( aligned C₁ & =4 ₀ [ R₁ R₂ R₂-R₁ +R₂ ]=4 ₀ [ 2 5 5-2 +5 ] C₁ & =4 ₀ 25 3 Farad aligned ) and (C₂=4 ₀ R₁ R₂ R₂-R₁ =4 ₀ 2 5 5-2 =4 ₀ 10 3 ) ( C₁ C₂ = 25 3 10 3 = 25 10 = 5 2 ) Hence, the correct option is (