Capacitors in Series & Parallel
Add capacitors in parallel or combine reciprocals in series — total capacitance, with the steps.
3 capacitors in parallel.
Capacitors are the mirror image of resistors. In parallel they add: 10 + 22 + 47 = 79 µF. In series you sum the reciprocals and invert — three 10 µF caps give 1 ÷ (1/10 + 1/10 + 1/10) = 1 ÷ (3/10) = 3.333 µF. Parallel raises capacitance; series lowers it.
Series vs parallel capacitance
How capacitors combine depends on how they are wired — and it is exactly backwards from resistors. In a parallel bank every capacitor shares the same voltage, so their stored charge adds and the capacitances add directly. In a series string the same charge sits on each capacitor while the voltage divides across them, so it is the reciprocals (1/C) that add, then you invert. Parallel gives you more total capacitance; series gives you less.
Parallel capacitances add directly; series reciprocals (1/C) add, then invert for C.
Worked example
Combine three 10 µF capacitors in series:
- 1 Pick the wiring. Parallel → add capacitances. Series → add reciprocals, then invert. Here the three caps are in series.
- 2 Sum the reciprocals. 1/C = 1/10 + 1/10 + 1/10 = 3/10 per microfarad.
- 3 Invert to get C. C = 1 ÷ (3/10) = 10/3 ≈ 3.333 µF.
- 4 Sanity-check. n equal capacitors in series give C ÷ n = 10 ÷ 3 ≈ 3.333 µF — smaller than any single cap, as series always is.
Capacitors vs resistors at a glance
Capacitors combine the opposite way to resistors. Series lowers capacitance; parallel raises it.
| Property | Series | Parallel |
|---|---|---|
| Total capacitance | 1/C = 1/C₁ + 1/C₂ + ⋯ | C = C₁ + C₂ + ⋯ |
| Two capacitors | C = C₁C₂ ÷ (C₁ + C₂) | C = C₁ + C₂ |
| Shared quantity | Same charge on each | Same voltage across each |
| Total vs each | Smaller than the smallest cap | Larger than any single cap |
| Resistors do the... | opposite (resistors add) | opposite (resistors take reciprocals) |
Why capacitors are the opposite of resistors
Capacitance is proportional to plate area. Wiring capacitors in parallel is electrically like widening the plates — more area means more charge stored per volt, so the capacitances add, just as parallel resistors would instead halve resistance. Put capacitors in series and you effectively stack the dielectric gaps, increasing the spacing between the outer plates; wider spacing means less capacitance, so the series total drops below the smallest capacitor. Resistance depends on length rather than area, which is why the two components behave in mirror image.