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

Answer

D

Explanation

Case I When the capacitors are joined in series,
`U_("series")=(1)/(2)(C_(1))/(n_(1))(4V)^(2)`
Case II When the capacitors are joined in parallel,
`U_("parallel")=(1)/(2)(n_(2)C_(2))V^(2)`
Given,`" "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))`