Capacitors in parallel
Almost every circuit board pairs a large electrolytic with a small ceramic across the same rail. In capacitance terms the ceramic adds almost nothing — 100 nF beside 100 µF is a rounding error. It is there for its low inductance at high frequency, which the big electrolytic cannot manage. The parallel sum is the right arithmetic and the wrong way to think about that pairing.
Capacitors in parallel add directly: C = C₁ + C₂ + … A 100 µF, 47 µF and 10 µF in parallel total 157 µF. This is the exact opposite of resistors, where parallel means a reciprocal sum.
How to combine capacitors in parallel
The mirror-image behaviour of capacitors and resistors follows from what each quantity measures. Resistance opposes current, so extra paths reduce it. Capacitance stores charge, so extra plates increase it — parallel capacitors are effectively one capacitor with a larger plate area. The important practical consequence is voltage rating: in parallel every capacitor sees the full supply voltage, so the lowest-rated part sets the limit for the whole bank, unlike series where the voltage divides.
Questions
C_total = C₁ + C₂ + … Straight addition, unlike resistors.