A series combination of `n_(1)` capacitors, each of value `C_(1)`, is charged by a source of potential difference `4 V`. When another parallel combination of `n_(2)` capacitors, each of value `C_(2)`, is charged by a source of potential difference `V`, it has same (total) energy stored in it, as the first combination has. the value of `C_(2)`, in terms of `C_(1)`, is then

Options

A. `(2C_(1))/(n_(1) n_(2))`
B. `16 (n_(2))/(n_(1)) C_(1)`
C. `2 (n_(2))/(n_(1)) C_(1)`
D. `(16C_(1))/(n_(1) n_(2))`

Answer

D

Explanation

`C_(s) = (C_(1))/(n_(1)) , C_(p) = n_(2) C_(2)`
`E_(s) = (1)/(2) C_(s) (4V)^(2) = (1)/(2) (C_(1))/(n_(1)). 16 V^(2) = (8 C_(1) V^(2))/(n_(1))`
`E_(p) = (1)/(2) C_(p) V^(2) = (1)/(2) n_(2) C_(2) V^(2)`
As `E_(p) = E_(s) :. (1)/(2) n_(2) C_(2) V^(2) = (8 C_(1) V^(2))/(n_(1))`
`C_(2) = (16C_(1))/(n_(1) n_(2))`