Two identical air capacitors A and B are connected in series across a battery of voltage V . While the battery remains connected, a dielectric slab of dielectric constant K = 2 is fully inserted into capacitor B . The ratio of the total energy stored in the system before the insertion of the dielectric to the total energy stored after the insertion is:

Step-by-step solution

Let the initial capacitance of each air capacitor be C . Initially, capacitors A and B are in series. The equivalent capacitance is: C_ eq,i = C C C + C = C 2 The total initial energy stored in the system is: U_i = 1 2 C_ eq,i V^2 = 1 2 ( C 2 ) V^2 = CV^2 4 When a dielectric of K = 2 is inserted into capacitor B , its new capacitance becomes C_B' = 2C . Capacitor A remains C_A = C . The new equivalent capacitance of the series combination is: C_ eq,f = C_A C_B' C_A + C_B' = C 2C C + 2C = 2C 3 Since the battery rema