About Capacitors in Series
A capacitor stores electric charge on two conductive plates separated by an insulator, and its capacitance C (in farads) relates the charge it holds to the voltage across it: C = Q/V. When two or more capacitors are wired end-to-end in a single chain — the output terminal of one connected directly to the input terminal of the next — they are in series. Series wiring behaves very differently from parallel wiring, and the equivalent capacitance always ends up smaller than the smallest individual capacitor.
Understanding the formula
In a series chain, the same current flows through every capacitor, so each one accumulates exactly the same charge Q. The total voltage across the chain is the sum of the individual voltages: V = V1 + V2 + V3 + ... Since each Vi = Q/Ci, dividing through by the shared Q gives the reciprocal (harmonic) addition rule: 1/C_eq = 1/C1 + 1/C2 + 1/C3 + ... + 1/Cn. For exactly two capacitors this reduces to the convenient product-over-sum shortcut C_eq = (C1 × C2) / (C1 + C2). Because reciprocals are being added, C_eq is always less than whichever individual capacitor is smallest — physically, stacking capacitors in series is equivalent to increasing the effective distance between the outermost plates, which lowers overall capacitance.
Working with units and the charge/voltage split
- Capacitance is commonly specified in picofarads (pF), nanofarads (nF), microfarads (µF), or farads (F) — 1 F = 10³ mF = 10⁶ µF = 10⁹ nF = 10¹² pF. Convert all capacitors to the same unit before combining them, which is what the unit selector above does automatically.
- Once you know C_eq and the applied voltage V, the shared charge is Q = C_eq × V (in coulombs when C is in farads and V is in volts).
- Each capacitor's individual voltage is then Vi = Q / Ci — smaller capacitors pick up a larger share of the total voltage, and the individual voltages always sum back to the applied voltage V.
Practical notes and common mistakes
Series capacitor banks are used in real circuits to raise the effective working voltage rating (splitting voltage across several capacitors so no single one exceeds its rated voltage) and to fine-tune an odd capacitance value from standard parts. A frequent mistake is applying the resistor-in-series rule (simple addition) to capacitors — capacitors do the opposite of resistors: they add directly in parallel and combine by reciprocals in series. Another common error is forgetting that a "0" or blank value for an unused slot must be excluded from the reciprocal sum entirely, not treated as a capacitor of zero capacitance (which would make 1/C infinite and force C_eq to zero).