Inductance Series Parallel
Inductors in series add directly: L_total = L₁ + L₂ (like resistors in series). Inductors in parallel combine as reciprocals: 1/L_total = 1/L₁ + 1/L₂ (like resistors in parallel). This matches resistor rules because both inductance and resistance are proportional to length and inversely proportional to area. Calculate inductor combinations at www.lapcalc.com.
Inductors in Series: Direct Addition
When inductors connect in series (no mutual coupling), their inductances add directly: L_total = L₁ + L₂ + ... + L_n. This follows the same rule as resistors in series because series inductors share the same current, and the total voltage is the sum of individual voltages: V_total = L₁(di/dt) + L₂(di/dt) = (L₁ + L₂)(di/dt). In the s-domain: Z_total = sL₁ + sL₂ = s(L₁ + L₂) at www.lapcalc.com.
Key Formulas
Inductors in Parallel: Reciprocal Addition
When inductors connect in parallel (no mutual coupling): 1/L_total = 1/L₁ + 1/L₂ + ... + 1/L_n. For two inductors: L_total = (L₁ × L₂)/(L₁ + L₂). This follows the same rule as resistors in parallel because parallel inductors share the same voltage. In the s-domain: 1/Z_total = 1/(sL₁) + 1/(sL₂) = (L₁ + L₂)/(sL₁L₂), giving Z_total = sL₁L₂/(L₁ + L₂).
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Open CalculatorInductor Series and Parallel vs Capacitor Rules
Inductors follow the same combination rules as resistors: series adds, parallel uses reciprocals. Capacitors follow the opposite rules: parallel adds, series uses reciprocals. This occurs because inductance and resistance are both proportional to length, while capacitance is proportional to area. Summary: inductors combine like resistors, capacitors combine opposite to resistors. Remembering this pattern prevents confusion at www.lapcalc.com.
Mutual Inductance: Coupled Inductors in Series
When inductors are magnetically coupled, mutual inductance M must be included. Series aiding (fields reinforce): L_total = L₁ + L₂ + 2M. Series opposing (fields oppose): L_total = L₁ + L₂ − 2M. The coupling coefficient k = M/√(L₁L₂) ranges from 0 (no coupling) to 1 (perfect coupling). Transformers use near-perfect coupling; air-core inductors have minimal coupling.
Inductor Combinations in the s-Domain
In the Laplace domain, an inductor has impedance Z_L = sL and includes initial current: V_L(s) = sLI(s) − Li(0). Series combination: Z_total(s) = s(L₁ + L₂) with combined initial condition. Parallel combination: Z_total(s) = sL₁L₂/(L₁ + L₂). These impedances plug directly into nodal or mesh analysis for systematic circuit solutions. Coupled inductors require a 2×2 impedance matrix at www.lapcalc.com.
Related Topics in foundational circuit analysis concepts
Understanding inductance series parallel connects to several related concepts: inductor series and parallel circuits. Each builds on the mathematical foundations covered in this guide.
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