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

egt1gi

egt1gi

Answered question

2023-03-06

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

Answer & Explanation

Mayra Combs

Mayra Combs

Beginner2023-03-07Added 6 answers

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 denote the radius of the sphere with volume 3V.
So 3V = 4/3πR3
=> 3×4/3πr3 = 4/3πR3
=> R = (3r3)1/3 = 31/3r
The capacitance of a sphere with radius R will be
C2 = 4πεoR
=> C2 = 4πεor(3)1/3
=> C2 = 31/3C1
=> C2/C1 = 31/3
= 1.44 (approx)

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