60
mH
0.06
H
20
mH
50
%
60
mH
0.06
H
20
mH
50
%
The Inductors in Series Calculator computes the total inductance when two or three inductors are connected end-to-end in a series configuration. In a series circuit, the same current flows through every inductor, and the total inductance is simply the arithmetic sum of the individual inductances.
Series inductor combinations are fundamental building blocks in filter design, impedance matching networks, RF tuning circuits, and power supply smoothing stages. Understanding how inductance adds in series helps engineers select components and predict circuit behavior accurately.
When inductors are connected in series (assuming no mutual coupling), the total inductance is the direct sum of all individual inductances:
$$L_{total} = L_1 + L_2 + L_3 + \cdots + L_n$$
This relationship arises because the total voltage across the series combination equals the sum of the voltages across each inductor. Since $$V = L \frac{dI}{dt}$$ and the current $$I$$ is identical through all inductors in series, we get:
$$V_{total} = L_1 \frac{dI}{dt} + L_2 \frac{dI}{dt} + L_3 \frac{dI}{dt} = (L_1 + L_2 + L_3)\frac{dI}{dt}$$
Therefore $$L_{total} = L_1 + L_2 + L_3$$. This formula assumes negligible mutual inductance between the coils. If the inductors are physically close and their magnetic fields interact, a mutual inductance term $$\pm 2M$$ must be added for each pair, depending on whether the coupling aids or opposes. For most practical calculations with shielded or well-separated inductors, the simple sum formula is accurate.
The energy stored in the combined inductance is $$W = \frac{1}{2}L_{total}I^2$$, which equals the sum of the individual stored energies when all carry the same current.
The Total Inductance is displayed in millihenries (mH) and henries (H). A larger total inductance means greater opposition to changes in current (higher inductive reactance at any given frequency). In filter circuits, higher series inductance shifts the cutoff frequency lower. In power supplies, more series inductance provides better ripple smoothing but may also increase voltage drop under transient loads. If any inductor value is set to zero, it effectively acts as a short wire segment contributing no inductance.
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Three common RF choke values (10 mH, 22 mH, 47 mH) combine to give 79 mH total series inductance.
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Results
Two 100 mH inductors in series yield 200 mH. Set L₃ to 0 when using only two inductors.
Because the same current flows through every inductor, the individual voltage drops $$V_k = L_k \frac{dI}{dt}$$ add together by Kirchhoff's Voltage Law, giving $$L_{total} = \sum L_k$$.
Mutual inductance $$M$$ must be included. For two coupled inductors: $$L_{total} = L_1 + L_2 \pm 2M$$. The plus sign applies for aiding coupling (fields reinforce), the minus for opposing coupling.
Yes. Simply set unused inputs to zero and mentally extend the sum. The formula generalizes to any number of inductors: $$L_{total} = L_1 + L_2 + \cdots + L_n$$.
No. Addition is commutative, so rearranging the physical order does not change the total inductance (assuming negligible mutual coupling).
Inductive reactance is $$X_L = 2\pi f L$$. Higher total inductance raises the impedance at a given frequency, which is useful in low-pass filters and choke circuits.
Common uses include building custom inductance values not available as single components, multi-stage power supply filters, RF impedance matching, and creating tuned circuits with specific resonant frequencies.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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