A circuit consists of three capacitors C₁ = 2 F , C₂ = 3 F , and C₃ = 5 F connected in parallel. This entire parallel combination is connected in series with a fourth capacitor C₄ = 10 F across an unknown DC voltage source V . If the charge on capacitor C₁ is 12 C , the total voltage V of the source and the charge on capacitor C₄ respectively are:

Step-by-step solution

The capacitors C₁, C₂ , and C₃ are connected in parallel. The voltage across this parallel combination is the same for each capacitor. Voltage across the parallel group, V_p = Q₁ C₁ = 12 C 2 F = 6 V . The equivalent capacitance of the parallel group is: C_p = C₁ + C₂ + C₃ = 2 F + 3 F + 5 F = 10 F . The total charge on the parallel group is: Q_p = C_p V_p = 10 F 6 V = 60 C . Since capacitor C₄ is connected in series with the parallel group, it carries the same total charge as the parallel group. Therefore, the charg