When connected across a battery, a capacitor stores a charge of 50 C . After the gap between the plates is filled with a dielectric, a charge of 100 C flows through the battery. Determine the dielectric constant of the inserted material.

Step-by-step solution

Initial charge on the capacitor is given by Q_i = CV = 50 C . When a dielectric of dielectric constant K is inserted, the new capacitance becomes C' = KC . Since the battery remains connected, the potential difference V across the capacitor remains constant. Final charge on the capacitor is Q_f = C'V = KCV = K Q_i . The additional charge that flows through the battery is Q = Q_f - Q_i = 100 C . Therefore, the final charge is Q_f = 50 + 100 = 150 C . Using Q_f = K Q_i , we get 150 = K 50 . Solving for K , we get K =