Do capacitors in parallel add?

Yes. C_total = C₁ + C₂ + ... Parallel capacitors add directly because the effective plate area increases. This is opposite to resistors in parallel.

Why are capacitor rules opposite to resistor rules?

Because C is proportional to area/distance while R is proportional to distance/area. Parallel adds area (increases C, decreases R). Series adds distance (decreases C, increases R).

How does voltage divide across series capacitors?

Voltage is inversely proportional to capacitance: V_n = Q/C_n. The smaller capacitor gets more voltage. This is opposite to series resistors where larger R gets more voltage.

Series and Parallel Capacitors

Quick Answer

Capacitors in series combine as reciprocals: 1/C_total = 1/C₁ + 1/C₂ (total capacitance decreases). Capacitors in parallel add directly: C_total = C₁ + C₂ (total capacitance increases). This is opposite to resistor combination rules. Series increases voltage rating; parallel increases capacitance. Calculate capacitor combinations at www.lapcalc.com.

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Series and Parallel Capacitors: The Opposite of Resistors

Capacitor combination rules are the mirror image of resistor rules. Capacitors in parallel add directly (C_total = C₁ + C₂) — just like resistors in series. Capacitors in series use the reciprocal formula (1/C_total = 1/C₁ + 1/C₂) — just like resistors in parallel. This reversal occurs because capacitance is proportional to plate area (parallel adds area) and inversely proportional to distance (series adds distance between plates).

Key Formulas

Capacitors in Series: Reduced Capacitance, Higher Voltage Rating

When capacitors connect in series, the total capacitance decreases: 1/C_total = 1/C₁ + 1/C₂. For two equal capacitors C in series: C_total = C/2. The benefit is increased voltage rating — each capacitor shares the applied voltage, so the combination withstands higher voltage than any individual capacitor. Charge Q is the same on all series capacitors, with voltage dividing as V_n = Q/C_n. Smaller capacitance gets more voltage at www.lapcalc.com.

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Capacitors in Parallel: Increased Capacitance, Same Voltage

When capacitors connect in parallel, total capacitance adds: C_total = C₁ + C₂ + C₃. Each capacitor sees the same voltage but stores charge independently: Q_n = C_n × V. Total charge is Q_total = C_total × V. Parallel capacitors are used to increase energy storage (E = ½CV²), smooth power supply ripple, and provide local charge reservoirs for high-speed digital circuits. The voltage rating equals the lowest-rated capacitor.

Series vs Parallel Capacitors: When to Use Each

Use parallel capacitors when you need more capacitance at the same voltage — power supply filtering, energy storage, and bypass decoupling. Use series capacitors when you need higher voltage rating or precise capacitance values from standard parts. Mixed configurations achieve both goals. In audio crossover networks, series capacitors block DC while passing AC. In power electronics, series capacitors balance voltage across high-voltage strings at www.lapcalc.com.

Capacitor Combinations in the s-Domain

In the Laplace domain, a capacitor's impedance is Z_C = 1/(sC). Capacitors in series: Z_total = 1/(sC₁) + 1/(sC₂) = (C₁ + C₂)/(sC₁C₂), which corresponds to C_total = C₁C₂/(C₁ + C₂). Capacitors in parallel: Z_total = 1/(s(C₁ + C₂)), confirming C_total = C₁ + C₂. These impedance combinations feed directly into transfer function calculations for filters and timing circuits at www.lapcalc.com.

Frequently Asked Questions

Capacitance decreases in series. The reciprocal formula gives C_total that is always less than the smallest individual capacitor. This is opposite to resistors in series.

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