Which formula represents the capacitance for capacitors connected in series?

• A. C = C1 + C2 + ...
• B. 1/C = 1/C1 + 1/C2 + ...
• C. C = 1/C1 + 1/C2 + ...
• D. C = 1/(1/C1 + 1/C2 + ...)

Answer: (D)

When capacitors are in series, the same amount of charge flows through each one, and the voltages across them add up to the total voltage. Because they share the same charge, adding their inverse capacitances gives the total inverse capacitance. The combined capacitance is then the reciprocal of that sum: C_eq = 1 / (1/C1 + 1/C2 + …).

For example, two capacitors of 10 μF each in series give C_eq = 1 / (1/10 + 1/10) = 1 / 0.2 = 5 μF. This shows how the series arrangement reduces the overall capacitance below any individual capacitor.

The form 1/C = 1/C1 + 1/C2 + … is equivalent to the above, since solving for C gives the reciprocal expression. But the standard way to present the capacitance itself is C = 1 / (1/C1 + 1/C2 + …).

The alternative of adding the capacitances directly (C1 + C2 + …) applies to capacitors in parallel, not in series, so it isn’t correct for series connections. And writing C = 1/C1 + 1/C2 + … would mix units and not reflect how series capacitance behaves.