Three identical parallel plate capacitors C₁, C₂ and C₃ , each of capacitance C , are connected such that C₁ and C₂ are in series, and this combination is in parallel with C₃ . A battery of voltage V is connected across the entire combination and the system reaches steady state. While the battery remains connected, a dielectric medium of dielectric constant k=3 is inserted into C₁ , completely filling the space betwe

Step-by-step solution

Initially, C₁ and C₂ (each of capacitance C ) are in series across the battery of voltage V . The equivalent capacitance of this branch is C/2 . Since C₁ and C₂ are equal, the voltage V divides equally between them. The initial voltage across C₁ is V₁ = V/2 . The initial electrostatic energy stored in C₁ is: U_i = 1 2 C₁ V₁^2 = 1 2 C ( V 2 )^2 = 1 8 CV^2 When a dielectric of constant k=3 is inserted into C₁ , its new capacitance becomes C₁' = 3C . The battery remains connected, so the total voltage across the serie