Capacitor Series Parallel
Series (μF)
5
Parallel (μF)
20
How it works
Capacitors combine in the opposite way to resistors: parallel capacitors add directly (C_total = C₁ + C₂ + ...), while series capacitors combine as reciprocals (1/C_total = 1/C₁ + 1/C₂ + ...). This counterintuitive reversal reflects the physics: parallel capacitors share voltage while increasing plate area; series capacitors share charge while increasing effective gap.
**Voltage rating in series** Connecting capacitors in series increases the effective voltage rating — the voltage divides across the series string proportional to the inverse of capacitance. Two identical capacitors in series each see half the applied voltage. This is used to handle voltages exceeding individual component ratings. Warning: unequal capacitances cause unequal voltage sharing; a bleeder resistor network is required to prevent one capacitor from exceeding its rating.
**Why parallel increases capacitance** Capacitance C = ε × A / d (permittivity × area / gap). Parallel capacitors increase effective plate area, directly increasing capacitance. Bank capacitors in parallel to achieve values unavailable in a single component or to reduce ESR (equivalent series resistance) in power supply filters.
**Filtering applications** Bypass capacitors work in parallel with power supply rails to absorb high-frequency current transients. Large electrolytic capacitors (low frequency) are paralleled with small ceramic capacitors (high frequency) because their effective capacitance complements each other across frequency ranges. Series capacitors are used for AC coupling — blocking DC while passing AC signals.
**Charge on series capacitors** Series capacitors store identical charge (Q = C × V). The smaller capacitor in a series combination charges to a higher voltage: V = Q / C. This asymmetry is critical in design — the smallest capacitor in series determines the maximum charge storage.
Frequently Asked Questions
- Use two capacitors in parallel: a large electrolytic (100–470 µF) for bulk charge storage and low-frequency filtering, and a small ceramic (0.1 µF = 100 nF) for high-frequency decoupling placed as close as possible to the IC power pin. The large capacitor handles slow load changes; the small ceramic (with low ESL) handles fast digital switching transients. Optionally add a 10 nF or 1 nF ceramic for very high-frequency noise. This multi-tier approach is standard for digital IC power supplies.
- In a series chain, all capacitors store the same charge Q. Total voltage = Q/C1 + Q/C2 + ... = Q × (1/C1 + 1/C2 + ...). Since C_total = Q/V_total, the total is 1/(1/C1 + 1/C2 + ...). Adding capacitors in series is like adding more dielectric gap — increasing the effective plate separation reduces capacitance. Two identical 100 µF capacitors in series give 50 µF, not 200 µF. The benefit is doubled effective voltage rating, which is why capacitors are series-stacked for high-voltage applications.
- Equivalent Series Resistance (ESR) is the effective resistance in series with the ideal capacitance — caused by lead resistance, contact resistance, and dielectric losses. Low ESR is critical for: switching power supply output filters (high-ESR capacitors cause output voltage ripple and instability), audio amplifier coupling capacitors (ESR causes signal loss at high frequencies), and motor drive circuits (high ripple current through high-ESR capacitors generates heat). Aluminum electrolytic capacitors have ESR of 0.1–10Ω; polymer capacitors: 5–50 mΩ; ceramic capacitors: milliohms.
- Resonant frequency f₀ = 1/(2π√(LC)). For an LC low-pass filter with L = 10 µH and C = 100 µF: f₀ = 1/(2π × √(10×10⁻⁶ × 100×10⁻⁶)) = 1/(2π × 10⁻³) ≈ 159 Hz. Below resonance, the filter passes signals. Above resonance, it attenuates. At resonance, impedance is at minimum (series LC) or maximum (parallel LC). For power supply filters, resonance should be above the switching frequency or well below the lowest frequency to filter.