A 20 F capacitor is charged to 40 V and a 30 F capacitor is charged to 10 V using separate batteries. The batteries are then removed, and the two capacitors are connected in parallel such that plates of the same polarity are connected together. The final common potential across the combination is:

Step-by-step solution

Initial charge on the first capacitor, Q₁ = C₁ V₁ = 20 40 = 800 C . Initial charge on the second capacitor, Q₂ = C₂ V₂ = 30 10 = 300 C . Since plates of the same polarity are connected together, the total charge is conserved and adds up: Q_ total = Q₁ + Q₂ = 800 + 300 = 1100 C . The equivalent capacitance of the parallel combination is: C_ total = C₁ + C₂ = 20 + 30 = 50 F . The final common potential V_f is given by: V_f = Q_ total C_ total = 1100 50 = 22 V . Answer: 22 V