If volume of Earth is V and area of Earth is A, then its capacitance will be ......

Options

A. `4 pi epsilon (A)/(V)`
B. ` 4pi epsilon_(0) (V)/(A)`
C. `12 pi epsilon_(0) (A)/(V) `
D. `12 pi in_(0) (V)/(A)`

Answer

A, B

Explanation

By considering Earth as sphere `C = 4pi epsilon_(0)R `
Volume ` V = (4)/(3) pi R^(3)` and area A `= 4 pi R^(2)`
`:. (V)/(A) = (4//3pi R^(3) )/(4pi R^(2)) = (R)/(3)`
`:. R = (3V)/(A)`
`:. C = 4pi in_(0)xx(3V)/(A)`
`:. C = 12 pi in_(0)(V)/(A)`