Two identical capacitors, each of capacitance C , are connected in series across a battery of voltage V . The battery is then disconnected. A dielectric material of dielectric constant K is fully inserted into the space between the plates of one of the capacitors. If the total electrostatic energy stored in the system decreases to 75 % of its initial value, the value of K is :

Step-by-step solution

Initially, the equivalent capacitance of the two capacitors in series is: C_ eq1 = C 2 The total initial charge supplied by the battery is Q = C_ eq1 V . Since the battery is disconnected, this total charge Q remains constant. The initial electrostatic energy stored in the system is: U_i = Q^2 2C_ eq1 = Q^2 2(C/2) = Q^2 C When a dielectric of constant K is inserted into one capacitor, its capacitance becomes KC . The new equivalent capacitance is: C_ eq2 = C KC C + KC = KC K+1 The final electrostatic energy stored