Capacitors in parallel have what relationship for total capacitance?

• A. The product of the capacitances
• B. The reciprocal of the sum of reciprocals
• C. The sum of the reciprocals
• D. The sum of the capacitances

Answer: (D)

When capacitors are connected in parallel, the voltage across each one is the same, so charges add up. The total charge is Q_total = Q1 + Q2 + ... = C1 V + C2 V + ... = (C1 + C2 + ...) V. Since the equivalent capacitance C_eq is defined by Q_total = C_eq V, it follows that C_eq = C1 + C2 + ... . So the total capacitance in parallel is simply the sum of the individual capacitances. This differs from the series case, where the reciprocal of the total capacitance equals the sum of the reciprocals: 1/C_eq = 1/C1 + 1/C2 + .... For example, two capacitors of 2 µF and 3 µF in parallel give 5 µF.