Final answer:
The common potential after connecting two charged capacitors in parallel is calculated using the total initial charge and the equivalent capacitance, leading to the final voltage both capacitors will share.
Step-by-step explanation:
When two charged capacitors are connected in parallel and allowed to reach equilibrium, they will share a common potential. The final voltage (Vf) is determined by the principle of conservation of charge which states that the total charge before the connection (Qinitial) will be equal to the total charge after the connection (Qfinal). The formula Q = CV (where Q is the charge, C is the capacitance, and V is the voltage) is used to express this relationship.
To find the common potential, we initially calculate the charge on each capacitor: Q1 = C1V1 and Q2 = C2V2. The total charge is thus Qtotal = Q1 + Q2. The equivalent capacitance when two capacitors are connected in parallel is Ceq = C1 + C2.
The common potential can be calculated using the formula Vf = Qtotal / Ceq. This yields a value that represents the voltage both capacitors will share after they are connected.