Three identical capacitors `C_(1),C_(2)` and `C_(3)` have a capacitance of `1.0 mu F` each and they are uncharged initially. They are connected in a circuit as shown in the figure and `C_(1)` is then filled completely with a dielectric material of relative permittivity `epsilon_(r)`. The cell electromotive force (emf) `V_(0)=8V`. First the switch `S_(1)` is closed while the switch `S_(2)` is kept open. When the capacitor `C_(3)` is fully charged, `S_(1)` is opened and `S_(2)` is closed simultaneously. When all the capacitors reach equilibrium, the charge on `C_(3)` is found to be `5 mu c`. The value of `epsilon_(r)` = ____________.

Options

A. 1.5
B. 2.5
C. 2.2
D. 3

Answer

A

Explanation

`C_(2)=C_(3)=1muF , C_(1)=in_(r)muF`
Apply KVL `(8-q)/(1)=(q)/(in_(r))+(q)/(1)` . . (1)
Also, `8-q=5`
`therefore q=3` .. (2)
By (1) and (2) `in_(r)=(3)/(2)=1.5`