Two parallel plate capacitors of capacity C and 3 C are connected in parallel combination and charged to a potential difference 18 V . The battery is then disconnected and the space between the plates of the capacitor of capacity C is completely filled with a material of dielectric constant 9 . The final potential difference across the combination of capacitors will be _____ V .

Step-by-step solution

The charge on the capacitor is given by q = C V . Initial charge on C = 18 C V And initial charge on 3 C = 54 C V Let final common potential difference = V ' When a dielectric of dielectric constant k is introduced between the plates of the capacitor the capacitance becomes k times. Applying conservation of charge, 9 C V ' + 3 C V ' = 18 C V + 54 C V ⇒ 12 C V ' = 72 C V ⇒ V ' = 6   V