Definition
An inductor is a passive two-terminal component that stores energy in a magnetic field produced by current through a coil. Its inductance, measured in henries (H), relates the magnetic flux linkage to the current that creates it.
Learning objectives
- Explain why an inductor opposes changes in current and stores magnetic energy.
- Calculate induced voltage, stored energy, reactance and an L/R time constant.
- Combine inductors in series and parallel and account for winding resistance.
- Recognise saturation and test an inductor without exposing the circuit to switching spikes.
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Progressive explanation
Start with the plain-language idea, then move into the engineering detail. Each level stands on its own, so you can stop at the depth you need.
Beginner The core idea
An inductor is a coil of wire that behaves like a flywheel for current. Current through the coil creates a magnetic field, and that field stores energy. When the current tries to change quickly, the collapsing or expanding field generates a voltage that opposes the change. This is why an inductor resists a sudden rise in current and why switching one off can produce a high voltage spike.
Inductors are the heart of transformers, motors, relays, ignition coils and many filters. In DC circuits they eventually behave almost like a plain piece of wire, because once the current is steady the magnetic field is steady too. Their opposition is to change, not to steady current.
Inductors are the heart of transformers, motors, relays, ignition coils and many filters. In DC circuits they eventually behave almost like a plain piece of wire, because once the current is steady the magnetic field is steady too. Their opposition is to change, not to steady current.
Intermediate How it behaves in a circuit
The voltage across an inductor is proportional to the rate of change of current: v = L × di/dt. A steady current therefore produces zero ideal voltage, while a fast current change produces a large voltage. The stored magnetic energy is E = ½ L I², so energy grows with the square of current and can be substantial in motors and high-current coils.
In series, inductances add when their magnetic fields do not interact; in parallel, the reciprocal rule applies. A coil also has winding resistance, so a real inductor is modelled as an inductance in series with a resistance. When connected to a DC source through a resistor, the current rises with a time constant τ = L / R and approaches its final value asymptotically. In AC, inductive reactance Xl = 2π f L increases with frequency, so the inductor opposes high frequencies more than low ones.
In series, inductances add when their magnetic fields do not interact; in parallel, the reciprocal rule applies. A coil also has winding resistance, so a real inductor is modelled as an inductance in series with a resistance. When connected to a DC source through a resistor, the current rises with a time constant τ = L / R and approaches its final value asymptotically. In AC, inductive reactance Xl = 2π f L increases with frequency, so the inductor opposes high frequencies more than low ones.
Advanced Limits, assumptions, engineering detail
Real magnetics are limited by core saturation, hysteresis and eddy-current losses, copper losses and inter-winding capacitance. Saturation occurs when the core cannot support more flux: inductance falls sharply and current can rise much faster than expected. Ferrite, powdered iron and laminated steel cores trade permeability, loss and saturation behaviour differently, and an air gap is often introduced to store energy and stabilise inductance.
At high frequency a winding behaves as an RL network with parasitic capacitance; self-resonance and the quality factor Q describe how far the part departs from an ideal inductor. Reverse recovery, leakage inductance and stray coupling matter in switching converters and transformers. The voltage spike when current is interrupted, v = −L di/dt, is both a hazard to semiconductors and a useful principle in ignition systems, so suppression and clamping are designed together with the magnetic part.
At high frequency a winding behaves as an RL network with parasitic capacitance; self-resonance and the quality factor Q describe how far the part departs from an ideal inductor. Reverse recovery, leakage inductance and stray coupling matter in switching converters and transformers. The voltage spike when current is interrupted, v = −L di/dt, is both a hazard to semiconductors and a useful principle in ignition systems, so suppression and clamping are designed together with the magnetic part.
Formulas and variables
Induced voltage
v = L × di/dt
v Instantaneous voltage across the inductor · V
L Inductance · henry (H)
di/dt Rate of change of current · A/s
A 100 mH inductor with current rising at 50 A/s develops v = 0.1 × 50 = 5 V.
Stored magnetic energy
E = ½ × L × I²
E Stored energy · joule (J)
L Inductance · H
I Current · A
A 100 mH coil carrying 2 A stores 0.5 × 0.1 × 4 = 0.2 J.
Inductive reactance and L/R time constant
Xl = 2π × f × L ; τ = L / R
Xl Inductive reactance · Ω
f Frequency · Hz
L Inductance · H
τ Time constant · s
R Total series resistance · Ω
100 mH at 60 Hz has Xl = 2π × 60 × 0.1 ≈ 37.7 Ω; with 10 Ω, τ = 10 ms.
Units of measurement
| Quantity | Symbol | Unit |
|---|---|---|
| Inductance | L | henry (H) |
| Magnetic flux | Φ | weber (Wb) |
| Reactance | Xl | ohm (Ω) |
| Energy | E | joule (J) |
Worked examples
Worked example
Voltage across an inductor during a current ramp
Problem. The current through a 100 mH inductor rises uniformly from 0 A to 0.5 A in 10 ms. Find the induced voltage during the ramp.
Solution. di/dt = (0.5 − 0) / 0.010 = 50 A/s. v = L × di/dt = 0.1 × 50 = 5 V.
v = 5 V during the ramp; the polarity opposes the rise in current.
Worked example
Reactance and time constant
Problem. A 100 mH inductor with 10 Ω of series resistance is used at 60 Hz. Find its reactance and the L/R time constant.
Solution. Xl = 2π × 60 × 0.1 = 37.70 Ω. τ = L / R = 0.1 / 10 = 0.010 s.
Xl ≈ 37.7 Ω and τ = 10 ms; the current reaches about 63 % of its final value in one time constant.
Practical applications
- Filtering and smoothing current in power supplies and audio circuits
- Storing energy in switching converters and ignition systems
- Creating magnetic fields in motors, solenoids, relays and transformers
- Blocking high-frequency noise while passing DC or low frequencies
Automotive applications
Inductors appear as ignition coils, injector and solenoid windings, relay coils, blower and pump motors, and as filter chokes in control modules. The ignition coil deliberately uses the inductive kick to generate a high voltage, while every other coil needs a suppression path so the same kick does not destroy a driver. In modern vehicles, coil-on-plug modules and injector drivers are designed with close attention to inductance, resistance and flyback behaviour.
Industrial applications
Industrial equipment uses inductors as line reactors and dv/dt chokes for variable-frequency drives, as filter chokes in rectifiers, as windings of motors, transformers and contactors, and as energy-storage elements in switched-mode supplies. Reactors limit fault current and reduce harmonics; their saturation behaviour and thermal rating must be coordinated with the drive and protection settings.
Measurement procedure
- De-energise and isolate the circuit, then verify that no voltage remains before connecting a meter.
- Measure the winding resistance with a normal ohmmeter; an open circuit or a very different resistance indicates a failed winding.
- Use an LCR meter or a suitable bridge for inductance, ideally with the coil out of circuit so nearby magnetics do not affect the result.
- For a quick in-circuit check, a scope can show the voltage spike when the coil is switched, but never interrupt a live inductive circuit without a suppression path.
- Compare the part with a known-good unit and check for overheating, swollen windings or burnt insulation.
Common mistakes
- Interrupting current through a coil without a freewheeling path, producing a voltage spike that damages drivers or insulation.
- Assuming a coil with the correct DC resistance is healthy; shorted turns can leave resistance almost unchanged while inductance collapses.
- Ignoring saturation and expecting inductance to remain constant at any current.
- Measuring inductance in-circuit while nearby magnetic parts or parallel windings change the reading.
Safety considerations
- An inductor can generate a high voltage when its current is interrupted; use a freewheeling diode, RC snubber or varistor as appropriate.
- Coils store energy and can remain hot; allow cooling and treat terminals as hazardous until the circuit is isolated.
- Never open a current-carrying inductive circuit by hand or with an unrated switch: the arc and induced voltage can injure and damage equipment.
- In high-voltage systems, respect creepage, clearance and insulation ratings; a coil is not an isolation barrier unless it is designed as one.
Frequently asked questions
Why does an inductor oppose changes in current?
The current creates a magnetic field, and changing that field induces a voltage that opposes the change according to Lenz’s law. The faster the current tries to change, the larger the opposing voltage, so the inductor resists sudden changes but allows steady current.
Does an inductor do anything in a DC circuit?
Yes, during switching and transients. After the current becomes steady, an ideal inductor has no voltage across it and behaves like a wire; the winding resistance is what remains. In practice, its effect on start-up, ripple and switching behaviour is often the reason it is there.
What is inductor saturation?
Saturation is the point where the magnetic core cannot support more flux. Beyond it, inductance falls and current rises much faster, so the component no longer behaves as designed. Saturation can overheat the winding and damage the switching device.
How can I test an inductor in circuit?
With the circuit dead, measure winding resistance and compare with the expected value. For inductance, disconnect the coil and use an LCR meter. In-circuit dynamic checks with a scope are possible, but they require a safe switching arrangement and a suppression path.