JEE Advanced 2018 · Paper 1, Physics 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 $C_1$ is then filled completely with a dielectric material of relative permittivity $\epsilon_r$. The cell electromotive force (emf) $V_0 = 8$ V. 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 $\epsilon_r$ = ______.