A capacitor of capacitance C is charged to a potential V₀ using a battery. The battery is then removed, and the capacitor is connected in parallel to an uncharged capacitor of capacitance 2C . After the system reaches a steady state, a dielectric material of dielectric constant K is completely filled between the plates of the first capacitor (of capacitance C ). If the final common potential of the system becomes V₀

Step-by-step solution

The initial charge on the first capacitor is Q = C V₀ . Since the battery is removed, this total charge remains conserved throughout the process. When the uncharged capacitor 2C is connected in parallel, the total charge is shared, but the total amount remains Q = C V₀ . Next, a dielectric of constant K is inserted into the first capacitor. Its new capacitance becomes KC . The new equivalent capacitance of the parallel combination is: C_ eq = KC + 2C = (K + 2)C The final common potential V_f is given by: V_f = Q C_