Question

A series combination of `N_(1)` capacitors (each of capacity `C_(1)`) is charged to potential difference 3V. Another parallel combination of `N_(2)` capacitors (each of capacity `C_(2)`) is charged to potential difference V. The total energy stored in both the combinations is same, The value of `C_(1)` in terms of `C_(2)` is
A. `(C_(2)N_(1)N_(2))/(9)`
B. `(C_(2)N_(1)^(2)N_(2)^(2))/(9)`
C. `(C_(2)N_(1))/(9N_(2))`
D. `(C_(2)N_(2))/(9N_(1))`

Answer 1

Correct Answer - A
Given
`E_(s) =E_(p) `
`1/2 C_(s) V_(s)^(2) =1/2 C_(p) V_(p)^(2)`
`(C_(1))/(N_(1))(3V) ^(2)= C_(2) N_(2) V^(2)`
`(C_(1))/(N_(1))9v^(2) =C_(2) N_(2) V^(2)`
`therefore C_(1) =(N_(1) N_(2)C_(2))/(9)`