In a circuit, three capacitors C₁, C₂ and C₃ are connected in series in that order between terminals A and D . A fourth capacitor C₄ is connected between terminal A and the junction of C₂ and C₃ . A fifth capacitor C₅ is connected between terminal D and the junction of C₁ and C₂ . The capacitance values are given as C₁ = 4 F , C₂ = 10 F , C₃ = 6 F , C₄ = 2 F and C₅ = 12 F . The equivalent capacitance of the network b

Step-by-step solution

Let the junction of C₁ and C₂ be node B , and the junction of C₂ and C₃ be node C . The network can be redrawn to reveal a Wheatstone bridge configuration between terminals A and D . The arms connected to terminal A are C₁ (between A and B ) and C₄ (between A and C ). The arms connected to terminal D are C₅ (between B and D ) and C₃ (between C and D ). The central capacitor is C₂ (between B and C ). Checking the balance condition: C₁ C₅ = 4 12 = 1 3 C₄ C₃ = 2 6 = 1 3 Since C₁ C₅ = C₄ C₃ , the bridge is balanced. Th