Three identical capacitors $${C_1},{C_2}$$ and $${C_3}$$ have a capacitance of $$1.0\,\mu F$$ each and they are unchanged 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 $${\varepsilon _r}.$$ The cell electromotive force $$\left( {emf} \right)\,\,{V_0} = 8V.$$ 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 $${\varepsilon _r} = $$ _________________.

At time t = 0, a battery of 10 V is connected across points A and B in the given circuit. If the capacitors have no charge initially, at what time (in seconds) does the voltage across them becomes 4 V? (Take ln5 = 1.6, ln3 = 1.1)