Three identical parallel plate air capacitors are connected in series to a battery of e.m.f. V. If two capacitors are completely filled with dielectric material of constant k, then potential difference across the third capacitor will become

Step-by-step solution

Let the capacitance of each identical air capacitor be C . When two capacitors are completely filled with a dielectric material of constant k , their capacitances become kC and kC . The third capacitor remains an air capacitor with capacitance C . The equivalent capacitance C_ eq of the three capacitors connected in series is given by: 1 C_ eq = 1 kC + 1 kC + 1 C 1 C_ eq = 2 kC + k kC = k+2 kC C_ eq = kC k+2 The total charge Q drawn from the battery of e.m.f. V is: Q = C_ eq V = kCV k+2 In a series circuit, the cha