Three capacitors C₁ = 6 F , C₂ = 2 F , and C₃ = 4 F are connected to a 20 V DC source as shown in the given circuit diagram. Find the equivalent capacitance of the circuit and the charge stored on capacitor C₃ .

Step-by-step solution

From the circuit diagram, capacitors C₂ and C₃ are in parallel. Their equivalent capacitance is: C₂₃ = C₂ + C₃ = 2 F + 4 F = 6 F Capacitor C₁ is in series with C₂₃ . The equivalent capacitance of the circuit is: C_ eq = C₁ C₂₃ C₁ + C₂₃ = 6 6 6 + 6 = 3 F The total charge supplied by the source is: Q = C_ eq V = 3 F 20 V = 60 C The potential difference across the parallel combination of C₂ and C₃ is: V₂₃ = Q C₂₃ = 60 C 6 F = 10 V The charge stored on capacitor C₃ is: Q₃ = C₃ V₂₃ = 4 F 10 V = 40 C Answer: 3 F and 40 C