Five identical air-filled capacitors, each of capacitance C , are connected to form a Wheatstone bridge network between two terminals A and B . The equivalent capacitance of this initial network is C₀ . A dielectric material of dielectric constant K = 4 is then completely filled into the two capacitors that are directly connected to terminal A . What is the ratio of the new equivalent capacitance of the network to th

Step-by-step solution

Initially, the five identical capacitors form a balanced Wheatstone bridge. The central capacitor is ineffective, and the equivalent capacitance is C₀ = C C C + C + C C C + C = C 2 + C 2 = C . When a dielectric of K = 4 is introduced into the two capacitors connected to terminal A , their capacitances become 4C . Let the arms connected to terminal A be C₁ = 4C and C₂ = 4C . Let the arms connected to terminal B be C₃ = C and C₄ = C . The ratio of the adjacent arms is C₁ C₃ = 4C C = 4 and C₂ C₄ = 4C C = 4 . Since C₁