Question

By what factor does the capacitance of a metal sphere increase if it's volume is trippled?

Answer 1

Let the initial radius of the sphere be r

Capacitance of the sphere C1 = 4πεor

Now volume of the sphere V = 4/3πr3

Let R be the radius of the sphere having volume 3V

So 3V = 4/3πR3

=> 3×4/3πr3 = 4/3πR3

=> R = (3r3)1/3 = 31/3r

Capacitance of the sphere having radius R will be

C2 = 4πεoR

=> C2 = 4πεor(3)1/3

=> C2 = 31/3C1

=> C2/C1 = 31/3

= 1.44 (approx)