JEE Advanced 2018 — Paper 1 — Question 11

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 $C_{l}$ is then filled completely with a dielectric material of relative permittivity $\epsilon_{r}$. The cell electromotive force (emf) $V_{0}=8 \mathrm{~V}$. First the switch $S_{l}$ is closed while the switch $S_{2}$ is kept open. When the capacitor $C_{3}$ is fully charged, $S_{l}$ 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 $\epsilon_{r}=$ $\_\_\_\_\_$.