Inductive Reactance⚠ unverified
Electrical / Basic · Compute the reactance of an inductor at a given frequency
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| inductance | inductance | H | 1.0 | Inductance of the inductor |
| frequency | frequency | Hz | 1.0 | Operating frequency |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | Xl | henry * hertz | Inductive reactance, in ohms (Ohm) |
The science & history
Understanding the Parameters
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Inductance $L$ — how strongly the inductor opposes a change in current ($v = L\,di/dt$); larger $L$ means larger induced back‑EMF and thus higher reactance.
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Frequency $f$ — higher $f$ means the current changes faster, inducing more back‑EMF, so more voltage is needed for the same current (higher reactance).
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$X_L$ — the voltage‑to‑current amplitude ratio in ohms; it is the magnitude of the inductor's impedance $Z_L = j\omega L = j X_L$, the $+j$ encoding a $90^\circ$ phase shift.
Derivation (Approaching a Proof)
The defining relation of an inductor (from Faraday's law) is $v = L\,\dfrac{di}{dt}$. Drive it with a sinusoidal current $i(t) = I_m \sin(\omega t)$, with $\omega = 2\pi f$:
$$v(t) = L\,\frac{di}{dt} = \omega L\, I_m \cos(\omega t) = \omega L\, I_m \sin\!\big(\omega t + \tfrac{\pi}{2}\big).$$
The voltage is sinusoidal with amplitude $V_m = \omega L\, I_m$ and leads the current by $90^\circ$ (equivalently, the current lags). The reactance is the amplitude ratio:
$$X_L = \frac{V_m}{I_m} = \omega L = 2\pi f L.$$
Units. $(\text{1/s})(\text{H}) = (\text{1/s})(\text{V}\cdot\text{s/A}) = \text{V/A} = \Omega$ — genuinely ohms. (Note: the live calculator currently mislabels the output unit as "henry·hertz"; the physical unit is the ohm — flagged for calculator verification.)
History
Inductive reactance rests on Faraday's law of induction (1831) and Lenz's law, which give the inductor's voltage–current relation. As with capacitance, Steinmetz's phasor method (1893) recast it as the impedance $Z_L = j\omega L$, placing reactance on the same ohmic footing as resistance and making AC network analysis algebraic.
Related Concepts: Capacitive Reactance, Impedance, Inductor Energy, Power Factor
Notes: Registry calculator inductive-reactance (unverified). Ideal‑inductor result; real inductors
add winding resistance and, at high frequency, parasitic capacitance.