Combining capacitors
When a single capacitor of the right value is not available, or you need a higher voltage rating, you combine several. The rules are the mirror image of the rules for resistors.
In parallel, the capacitances add:
C = C₁ + C₂ + C₃ + …
In series, the reciprocals add:
1 ÷ C = 1 ÷ C₁ + 1 ÷ C₂ + 1 ÷ C₃ + …
A series combination is always smaller than the smallest capacitor in it. Enter 0 for any position you do not use; the calculator ignores it.
Charge and energy
The calculator also uses the voltage across the whole combination to find:
- the charge stored, Q = C × V
- the energy stored, E = ½ × C × V²
With capacitance in microfarads, the charge comes out in microcoulombs, and the energy is shown in millijoules.
Worked example
Three capacitors of 10 µF, 22 µF and 47 µF at 12 V:
| Parallel | Series | |
|---|---|---|
| Total capacitance | 79 µF | 5.998 µF |
| Charge | 948 µC | 71.97 µC |
| Energy | 5.688 mJ | 0.4318 mJ |
The parallel bank stores more than 13 times the energy of the series string at the same voltage.
Why use series at all?
The main reason is voltage. Each capacitor in a series string carries the same charge, so the total voltage divides between them in inverse proportion to their capacitance: V₁ = Q ÷ C₁. In the example, the 10 µF capacitor takes 7.2 V, the 22 µF one 3.3 V and the 47 µF one 1.5 V. Two identical capacitors in series split the voltage evenly, which lets you build a 50 V part from two 25 V ones. In practice, balancing resistors are placed across each capacitor because leakage currents are never exactly equal.
Why the rules are reversed
The capacitance of a plate capacitor is C = ε × A ÷ d. Putting capacitors in parallel effectively adds plate area A, so capacitance adds. Putting them in series effectively adds plate spacing d, so the reciprocals add. Resistors do the opposite because resistance grows with length and falls with cross-section.
Practical notes
Electrolytic capacitors have wide tolerances, often ±20%, so the real total can differ noticeably from the nominal value. Polarized capacitors must be connected the right way round in both arrangements, and the voltage rating of a parallel bank is that of its weakest member.