Three identical capacitors \( C_{1}, C_{2} \) and \( C_{3} \) have a capacitance of \( 1.0 \mu \mathrm{F} \) 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) \( V_{0}=8 \mathrm{~V} \). 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 \( 5 \mu \mathrm{C} \). The value of \( \epsilon_{r} \).
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