From 2 capacitors • Parallel: 30 μF • Series: 6.667 μF
Capacitors in parallel sit across the same two nodes, so every capacitor sees the same voltage. The total stored charge is the sum of each cap's charge, which makes the equivalent capacitance the simple sum. This is the OPPOSITE of resistors, where parallel resistors use the reciprocal sum.
C = C₁ + C₂ + … + Cₙ
Capacitors in series share a single charge path, so the same charge Q sits on every cap. The voltage divides across them, and the equivalent capacitance is always smaller than the smallest cap in the chain — found by adding reciprocals and inverting. Again the OPPOSITE of resistors, which sum directly in series.
1/C = 1/C₁ + 1/C₂ + … + 1/Cₙ
Capacitors combine using the OPPOSITE formulas from resistors — a fact that trips up nearly every student. In parallel, capacitors share the same voltage; charge stored on each cap simply adds (Q = CV), so capacitance ADDS in parallel. In series, the same charge has to flow onto every plate (charge conservation along an isolated wire); the voltage divides, and the equivalent capacitance is the RECIPROCAL sum — always smaller than the smallest cap. Use parallel to get a bigger bulk capacitance (filter caps, decoupling banks) and use series to derate the voltage stress across each cap or to fine-tune the total below a single available value.
You have a 10 μF capacitor and a 20 μF capacitor. Find the equivalent capacitance when they are connected (a) in parallel and (b) in series.
If the same 5 V is applied across both circuits, the parallel bank stores Q = CV = 30 μF · 5 V = 150 μC, while the series bank stores only Q = 6.667 μF · 5 V ≈ 33.3 μC (the same Q sits on each cap, with about 3.33 V across the 10 μF and 1.67 V across the 20 μF).
Three concepts make the series-vs-parallel choice click. First, charge vs voltage: in parallel the voltage is shared and the charges add; in series the charge is shared and the voltages add. That asymmetry is exactly what flips the formulas relative to resistors. Second, voltage division in series: voltage across each cap is inversely proportional to its capacitance (V_i = Q/C_i), so the smallest cap in a series chain gets the largest share of the total voltage — and is the first to fail if you exceed its rating. Designers either pick caps with margin or add balancing resistors. Third, voltage rating math for series stacks: total rated voltage = N × (lowest cap's rating) in the worst case. Two 100 V caps in series can safely handle about 200 V (ignoring tolerance), which is the whole reason series stacking is used in high-voltage power supplies despite the capacitance penalty.
Add the capacitance values directly: C = C₁ + C₂ + … + Cₙ. Two 10 μF caps in parallel give 20 μF; three 100 nF caps in parallel give 300 nF. Parallel capacitors share the same voltage and their stored charges add, so the equivalent capacitance is the simple sum.
Add the reciprocals and invert: 1/C = 1/C₁ + 1/C₂ + … + 1/Cₙ. For two caps the product-over-sum shortcut also works: C = C₁·C₂ / (C₁ + C₂). Series capacitors share the same charge and their voltages add; the equivalent capacitance is always smaller than the smallest cap in the chain.
The asymmetry comes from what is shared in each topology. Parallel components share voltage; for resistors that lets currents add (V = IR ⇒ I/V = 1/R sums), while for capacitors it lets charges add (Q = CV ⇒ Q/V = C sums). Series components share current (resistors) or charge (capacitors); the resistor voltage sums directly to give R series, but the capacitor voltage sums as Q/C — making 1/C the additive quantity. Capacitance behaves like the reciprocal of resistance with respect to series-parallel rules.
Series always DECREASES total capacitance below the smallest cap in the chain. Two identical caps in series give exactly C/2; N identical caps in series give C/N. If you need more capacitance, switch to parallel — that adds the values directly.
The same charge Q sits on every cap in series, and Vᵢ = Q / Cᵢ, so voltage is INVERSELY proportional to capacitance. The smallest cap in the chain takes the largest share of the applied voltage — and is the first to fail if you exceed its rating. High-voltage series stacks usually add balancing resistors in parallel with each cap to keep the voltage split even.
The combination rules are mirror-images. Resistors: SUM in series, RECIPROCAL SUM in parallel. Capacitors: RECIPROCAL SUM in series, SUM in parallel. Numerically, R = 10 Ω with R = 20 Ω gives 30 Ω in series and ~6.67 Ω in parallel; C = 10 μF with C = 20 μF gives 30 μF in parallel and ~6.67 μF in series. Same numbers, swapped topologies.
Yes — but the voltage will split unevenly. With C₁ = 1 μF and C₂ = 10 μF in series across 110 V, the 1 μF cap sees 100 V while the 10 μF cap sees only 10 V (voltage inversely proportional to capacitance). Check each cap's individual voltage rating, not just the sum, and use balancing resistors for high-voltage applications.
Use PARALLEL when you need more total capacitance, lower ESR, or extra filtering bandwidth — typical in power-supply bulk filtering and decoupling. Use SERIES when you need to handle a voltage higher than any single cap can withstand (with balancing), or when you want a smaller equivalent capacitance built from larger available values. Series is also common in DC-blocking applications where you want to derate voltage stress across cheap, high-value caps.
Reference: Standard electrical-circuit identities: parallel capacitances add (charges sum at common-voltage nodes); series capacitances combine by reciprocal sum (voltages sum across a common-charge path). Inverse of the resistor series-parallel rules.
The two series–parallel combination rules for capacitors are mirror-images of the rules for resistors — the same shapes, swapped between topologies:
Where:
Two capacitors in series is common enough that the “product over sum” shortcut applies: C = C₁·C₂ / (C₁ + C₂). For three or more series caps you must use the full reciprocal sum.
Power Supply Filter Bank
A power-supply designer parallels three 1000 μF electrolytics across the DC rail to drop ESR and raise bulk capacitance.
Equivalent capacitance ≈ 3000 μF (3 mF).
Parallel banks of identical caps also drop the equivalent ESR by a factor of N — useful for low-impedance bulk filtering at high currents.
High-Voltage Stacking
You need to handle 600 V DC but only have 400 V-rated, 470 μF electrolytics. Stack two in series to share the voltage.
Series stack ≈ 235 μF rated for ~800 V (with balancing).
Series stacks lose half the capacitance to gain double the voltage — the classic tradeoff. Modern film caps simplify HV stacking, but electrolytics still dominate cost-sensitive designs.
Decoupling Network
On a digital board you often see a 10 μF bulk cap parallel with a 100 nF ceramic across every IC power pin.
Total static capacitance ≈ 10.1 μF, but the win is bandwidth, not magnitude.
On large parallel cap banks, watch for parallel-resonance peaks between the bulk and bypass caps — pick values an order of magnitude apart and add a small damping resistor if needed.
| Topology | Resistors | Capacitors |
|---|---|---|
| Series | R = R₁ + R₂ + … (add) | 1/C = 1/C₁ + 1/C₂ + … (reciprocal sum) |
| Parallel | 1/R = 1/R₁ + 1/R₂ + … (reciprocal sum) | C = C₁ + C₂ + … (add) |
| Shared quantity | series: current · parallel: voltage | series: charge · parallel: voltage |
The asymmetry comes from what the components share. Parallel elements share voltage in both cases. In series, resistors share current (V sums directly ⇒ R adds), while capacitors share charge (V = Q/C sums ⇒ 1/C adds).