Inductive Reactance
Opposition of an inductor to AC.
Formula
Variables
How it works
An inductor resists changes in current because a changing current creates a changing magnetic field, which in turn induces a back-emf that opposes the change. In AC circuits, the current is continuously reversing, so this opposition appears as an effective resistance called inductive reactance. The factor of 2\pi f comes from the rate of change in sinusoidal signals: higher frequency means the current changes direction faster, so the inductor opposes it more strongly; larger inductance also increases the induced back-emf.
When to use it
Use this formula when analyzing AC circuits that contain coils, chokes, transformers, motors, or any inductive component. It is especially useful for finding current, phase behavior, or impedance in frequency-dependent circuit problems.
Worked example, step by step
Given: Frequency, f = 400 Hz Inductance, L = 18 mH = 0.018 H Step 1: Write the formula X_L = 2\pi f L Step 2: Substitute the values X_L = 2\pi(400)(0.018) Step 3: Calculate X_L = 2\pi(7.2) X_L = 45.24 \Omega Final answer: The inductive reactance is X_L \approx 45.2 \Omega.
Common mistakes to avoid
- Forgetting to convert millihenries or microhenries into henries before calculating
- Using this formula for DC circuits, where steady-state inductive reactance is not applied the same way
- Mixing up reactance with resistance and assuming it dissipates power like an ordinary resistor
Did You Know?
An inductor passes low frequencies and blocks high ones, exactly opposite to a capacitor.
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