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General

Series / Parallel Resistor, Capacitor & Inductor Calculator

Calculate the equivalent series and parallel combination of up to four resistors, capacitors, or inductors. Also computes the voltage divider ratio for two-resistor networks.

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Formula

Rseries=R1+R2+…,1Rparallel=1R1+1R2+…R_{series} = R_1 + R_2 + \ldots, \quad \frac{1}{R_{parallel}} = \frac{1}{R_1} + \frac{1}{R_2} + \ldots
R_series— Total series resistance / inductance (Ω or μH)
R_parallel— Total parallel resistance / inductance (Ω or μH)
C_series— 1/C_total = 1/C1 + 1/C2 (caps in series) (nF)
C_parallel— C_total = C1 + C2 (caps in parallel) (nF)

How It Works

Series-parallel resistor calculator computes equivalent resistance for combined networks — essential for voltage dividers, current sharing, and impedance matching. Circuit designers and PCB engineers use this to create non-standard resistance values from E24/E96 series components and to distribute power dissipation across multiple parts. Per Horowitz & Hill 'Art of Electronics' (3rd ed., Ch.1), series resistors sum directly (R_total = R1 + R2 + ... + Rn), while parallel resistors follow the reciprocal rule (1/R_total = 1/R1 + 1/R2 + ... + 1/Rn). For two parallel resistors, the simplified formula R_total = (R1 × R2)/(R1 + R2) is used in over 90% of practical applications. Power dissipation splits proportionally: series resistors dissipate power proportional to their resistance; parallel resistors dissipate power inversely proportional to resistance.

Worked Example

Design a precision 7.5kΩ resistance using E24 series (5%) components. Option 1 (series): 6.8kΩ + 680Ω = 7.48kΩ (0.27% error). Option 2 (parallel): Two 15kΩ resistors = 7.5kΩ exactly. For the parallel option, each resistor carries half the current, so power dissipation is halved — with 10mA total current, each 15kΩ resistor dissipates P = I²R = (5mA)² × 15kΩ = 0.375W versus a single resistor dissipating 0.75W. Per IPC-2221B derating guidelines, the parallel configuration allows smaller 0.5W resistors instead of a single 1W resistor, reducing PCB footprint by approximately 40%.

Practical Tips

  • ✓To create non-standard values: use series for values above available stock, parallel for values below — a 3.3kΩ parallel with 10kΩ yields 2.48kΩ
  • ✓For precision voltage dividers, use matched resistor networks (0.1% ratio accuracy) instead of discrete parts — Vishay MPM series achieves 0.05% matching
  • ✓Verify parallel power sharing: the resistor with lowest value gets highest power — P_n = V² / R_n for parallel resistors sharing voltage V

Common Mistakes

  • ✗Using series formula for parallel networks — results in values 2-10× too high; parallel resistance is always less than the smallest individual resistor
  • ✗Neglecting power distribution in parallel networks — resistor with lowest value carries highest current and may overheat if undersized
  • ✗Assuming tolerance errors cancel — worst-case tolerance analysis shows combined 5% resistors can yield 7% total error per root-sum-square method

Frequently Asked Questions

Parallel paths increase total conductance (G = 1/R). Two 10kΩ resistors in parallel provide G_total = 2 × (1/10kΩ) = 0.2mS, giving R_total = 5kΩ. This is equivalent to doubling the conductor cross-sectional area per Pouillet's law.
Capacitors follow inverted rules: series capacitors combine like parallel resistors (1/C_total = 1/C1 + 1/C2), parallel capacitors sum directly (C_total = C1 + C2). This is because capacitance is proportional to plate area (parallel increases area) per the parallel-plate capacitor formula C = εA/d.
Yes, mixing values is standard practice. For optimal noise performance, IEEE 802.3 specifies matched impedances — for example, 100Ω differential Ethernet uses two 50Ω resistors in series for termination rather than one 100Ω to improve common-mode rejection by 6dB.
Digital multimeters (Fluke 87V: 0.05% accuracy) measure total resistance directly. SPICE simulation validates complex networks — LTspice is free and handles networks with 10,000+ components.
Use root-sum-square (RSS) for typical error: two 5% resistors yield √(5² + 5²) = 7.07% worst-case. For voltage dividers, matched resistor arrays (Vishay, Bourns) achieve ratio tolerance of 0.05% regardless of absolute accuracy.

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