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Capacitors in series experience the same charge Q but different voltages; total voltage: V_total = Q(1/C₁ + 1/C₂ + ...). Capacitors in parallel have the same voltage but different charges; total charge: Q_total = V(C₁ + C₂ + ...). For series: 1/C_eq = 1/C₁ + 1/C₂ + .... For parallel: C_eq = C₁ + C₂ + ....
From your study of energy stored in capacitors, you know that a capacitor with capacitance C charged to voltage V holds charge Q = CV and stores energy U = ½CV². When you connect capacitors together, the same fundamental constraint — Q = CV — applies to each device, but the network arrangement determines which quantities are shared and which differ.
Parallel connection is the simpler case to understand first. Connecting two capacitors in parallel means their terminals are wired together, so both capacitors face exactly the same voltage V across their plates. Each capacitor independently draws the charge it needs: Q₁ = C₁V and Q₂ = C₂V. The total charge drawn from the source is Q_total = Q₁ + Q₂ = (C₁ + C₂)V. From the source's perspective, this looks like a single capacitor with C_eq = C₁ + C₂. Adding capacitors in parallel simply adds their capacitances — intuitive because you are effectively increasing the total plate area available to store charge.
Series connection requires more careful reasoning. When you charge a series combination, charge cannot accumulate on the middle plates; every electron that arrives on the outer plate of C₁ repels an equal charge off the inner plate of C₁, which charges the inner plate of C₂. The result is that both capacitors end up with exactly the same charge Q, regardless of their individual capacitances. The voltages, however, differ: V₁ = Q/C₁ and V₂ = Q/C₂. The total voltage is V₁ + V₂ = Q(1/C₁ + 1/C₂), so 1/C_eq = 1/C₁ + 1/C₂. Notice that the equivalent capacitance is always smaller than either individual capacitor — series connection is like increasing the plate separation, which reduces C.
A useful memory anchor: series and parallel combination rules for capacitors are the *opposite* of the rules for resistors. Resistors in series add directly; capacitors in parallel add directly. This is not a coincidence — it reflects the dual relationship between charge storage and current flow. In real circuits, these combination rules let you replace any network of capacitors with a single equivalent capacitance, which enormously simplifies energy storage calculations and circuit analysis.