In the following circuit two identical capacitors, a battery and a switch (s) are connected as shown. The switch (s) is opened and dielectric of constant `(K=3)` are inserted in the condensers. The ratio of electrostatic energies of the system before and after filling the dielectric will be.
.

Options

A. `3 : 1`
B. `5 : 1`
C. `3 : 5`
D. `5 : 3`

Answer

C

Explanation

`:. U_(1)=(1)/(2) CV^(2)+(1)/(2)CV^(2)=CV^(2)`
`:. U_(2)=(1)/(2) xx3xxCV^(2) +(1)/(2) xx3C(V^(2))/(9)=(5)/(3) CV^(2)`
`:. (U_(1))/(U_(2))=(3)/(5)`.