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. `(16 C_(1))/(n_(1)n_(2))`

Answer

D

Explanation

Case I. When the capacitors are connected in series
`U_("series") = (1)/(2) (C_(1))/(n_(1))(4V)^(2)`
Case II. When the capacitors are connected in parallel
`U_("parallel") = (1)/(2) (n_(2)C_(2)) V^(2)`
According to question, `U_("series") = U_("parallel")`
or `= (1)/(2)(C_(1))/(n_(1)) (4V)^(2) = (1)/(2) (n_(2)C_(2)) V^(2)`
`rArr C_(2) = (16C_(1))/(n_(2)n_(1))`