Inductors

Learning Objectives

By the end of this page, you should be able to:

• Define inductance and explain how an inductor stores energy in a magnetic field
• Apply the inductor voltage-current relationship V = L(dI/dt) to circuit problems
• Distinguish air-core, iron-core, ferrite-core, and toroidal inductors by application
• Calculate inductive reactance and explain how it changes with frequency
• Explain why inductors oppose changes in current, and connect this to real circuit behaviour like flyback voltage spikes
• Describe at least three practical applications of inductors, including filters and transformers

Quick Answer

An inductor is a passive two-terminal component — typically a coil of wire around a core — that stores energy in a magnetic field when current flows through it. It resists any change in current: increase the current and it fights back with an opposing voltage; decrease it and it tries to keep current flowing. This behaviour is described by V = L(dI/dt), where L is the inductance in henries. Because inductors oppose fast current changes but allow steady current to flow freely, they are the natural partner to capacitors for filtering: inductors block high frequencies and pass DC, the opposite of a capacitor. You'll find them in power supply filters, radio tuning circuits, transformers, and motor windings.

What Is an Inductor?

An inductor is usually just a coil of wire, sometimes wound around a core of iron, ferrite, or another magnetic material. When current flows through the coil, it generates a magnetic field around the wire. If that current changes, the magnetic field changes too, and by Faraday's law of electromagnetic induction, a changing magnetic field induces a voltage (EMF) in the coil itself. That induced voltage always opposes the change that created it — a phenomenon known as Lenz's law — which is why an inductor resists changes in current rather than resisting current itself (that's what a resistor does).

This relationship is captured by:

V = L × (dI/dt)

Where:

• V is the voltage induced across the inductor
• L is the inductance, measured in henries (H)
• dI/dt is the rate of change of current over time

If current is steady (DC, not changing), dI/dt is zero, so an ideal inductor produces no voltage drop — it behaves like a plain wire. This is the mirror image of a capacitor, which blocks steady DC but passes changing signals.

The inductance value itself depends on the coil's physical construction:

L = N² × μ × A / l

Where N is the number of turns, μ is the permeability of the core material, A is the cross-sectional area, and l is the coil's length. More turns, a higher-permeability core, or a larger cross-section all increase inductance.

How Inductors Behave in a Circuit

Think of an inductor as having "electrical inertia." Just as a moving object resists a sudden change in velocity, an inductor resists a sudden change in current.

• When current tries to increase suddenly (like when you first close a switch), the inductor generates a back-EMF that opposes the rise, so current ramps up gradually rather than jumping instantly.
• When current is suddenly interrupted (like opening a switch on an energized coil), the collapsing magnetic field induces a large voltage spike trying to keep current flowing — this is the well-known "flyback" spike that can arc across switch contacts or destroy a transistor if not managed with a flyback diode.

This same behaviour is why inductors are ideal for smoothing current in switching power supplies: they resist the rapid current pulses from a switching transistor and deliver a smoother, more continuous current to the load.

Types of Inductors

Air-Core Inductors

Simplest form — just a coil with no magnetic core. Low inductance values, but no core losses, making them suitable for high-frequency RF circuits.

Iron-Core Inductors

Wrapping the coil around an iron core dramatically increases inductance because iron has high permeability. Lower cost, but iron cores suffer losses (hysteresis and eddy currents) at high frequencies, so these are best for low-frequency power applications like mains transformers.

Ferrite-Core Inductors

Ferrite is a ceramic magnetic material with high permeability and much lower eddy-current losses than iron at high frequencies, making these the go-to choice for switching power supplies and RF chokes.

Powdered Iron-Core Inductors

A compromise: powdered iron particles bonded together reduce eddy-current losses compared to solid iron while still giving high inductance. Common in power supply filter inductors.

Toroidal Inductors

Wound on a donut-shaped core, keeping the magnetic field mostly contained within the core loop. This minimizes electromagnetic interference with nearby components and gives a compact, efficient design — common in switch-mode power supplies and audio equipment.

Variable Inductors

Inductance can be mechanically adjusted, often by moving a ferrite slug in or out of the coil — used for fine-tuning resonant circuits.

Inductors at DC vs AC

An inductor's opposition to current — its reactance — depends on frequency:

X_L = 2πfL

At DC (f = 0), reactance is zero, so an ideal inductor acts like a plain wire. As frequency increases, reactance increases, so an inductor increasingly opposes current flow. This is exactly opposite to a capacitor's behaviour, and it's why the two are often paired:

• Low-pass filters: An inductor in series passes DC and low frequencies while blocking higher frequencies.
• RF chokes: A high-reactance inductor blocks unwanted high-frequency noise from traveling along a power line while letting DC power through.
• Resonant circuits: Paired with a capacitor, an inductor forms an LC tank circuit that resonates at a specific frequency, f₀ = 1/(2π√(LC)) — the basis of radio tuning.

Real-World Example

Inside a switch-mode phone charger, a small ferrite-core inductor sits right after the switching transistor. The transistor turns on and off rapidly (often hundreds of kilohertz), and the inductor smooths those on/off current pulses into a much steadier DC current before it reaches the output capacitor and, ultimately, your phone's battery. Without the inductor, the output would be a chopped, noisy waveform instead of clean DC.

Applications of Inductors

• Filtering: Combined with capacitors in low-pass, high-pass, and band-pass filters
• Transformers: Two coupled inductors transfer energy between circuits with voltage/current transformation and electrical isolation
• Switching power supplies: Smooth pulsed current from a switching transistor into steady DC
• RF chokes: Block high-frequency noise from power lines
• Oscillators and tuning circuits: LC tank circuits set the resonant frequency of radio transmitters and receivers
• Motors and relays: The coil windings that generate magnetic fields for mechanical work

Circuit Behaviour: LC Resonance

In a series or parallel LC circuit, energy sloshes back and forth between the inductor's magnetic field and the capacitor's electric field. At the resonant frequency f₀ = 1/(2π√(LC)), this energy exchange is most efficient, giving the circuit a sharp peak (or notch) in its frequency response — the working principle behind radio channel selection.

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Key Terms

Term	Definition	Related Concept
Inductance (L)	Property of a coil that opposes change in current, measured in henries (H)	Faraday's law
Back-EMF	Voltage induced by an inductor opposing a change in current	Lenz's law
Inductive reactance (X_L)	Opposition to AC current, X_L = 2πfL, increases with frequency	Filtering
Air-core inductor	Coil with no magnetic core; low inductance, good for RF	High-frequency circuits
Ferrite-core inductor	Coil around ceramic magnetic core; low loss at high frequency	Switching power supplies
Toroidal inductor	Coil wound on a donut-shaped core; low field leakage	Compact filter design
Flyback spike	Voltage surge from a collapsing magnetic field when current is interrupted	Transistor protection, flyback diodes
Q-factor	Ratio of reactance to resistance; measures efficiency/selectivity	Resonant circuits
Mutual inductance	Coupling between two coils, basis of transformer action	Transformers
Resonant frequency (f₀)	Frequency at which an LC circuit's energy exchange peaks; f₀ = 1/(2π√(LC))	LC tank circuits

Common Mistakes

Misconception: An inductor opposes current flow the same way a resistor does. Why it's wrong: A resistor opposes current itself, dissipating energy as heat regardless of whether current is steady or changing. An inductor opposes only changes in current; a steady DC current flows through an ideal inductor with no opposition at all. Correct understanding: Inductive opposition (reactance) exists only when current is changing, and increases with the rate of change (frequency): X_L = 2πfL.

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Misconception: It's safe to suddenly disconnect power from an energized coil (like a relay or motor) without any protection. Why it's wrong: The collapsing magnetic field induces a large voltage spike as the inductor tries to maintain current flow. This spike can be many times the supply voltage and can destroy switching transistors or cause arcing at switch contacts. Correct understanding: Always include a flyback (freewheeling) diode across an inductive load like a relay coil to give the collapsing field a safe path to dissipate its energy.

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Misconception: A bigger, heavier inductor core always means better performance. Why it's wrong: Core material choice matters more than size for a given frequency. An iron core that works well at 50/60 Hz mains frequency suffers severe eddy-current losses at hundreds of kilohertz, making it a poor (and overheating) choice for a switching supply, where a smaller ferrite core would perform better. Correct understanding: Match the core material to the operating frequency — iron for low-frequency power, ferrite or powdered iron for high-frequency switching and RF work.

Comparison and Connections

Feature	Air-Core	Iron-Core	Ferrite-Core	Toroidal
Inductance for given size	Low	High	Medium-high	Medium-high
Best frequency range	High (RF)	Low (mains, audio)	High (switching, RF)	Wide, compact
Core losses	None	High at high frequency	Low at high frequency	Depends on core material
Typical use	RF coils, antennas	Mains transformers	SMPS chokes	Compact filters, audio

Practice Questions

Recall

1. What is the formula relating voltage, inductance, and rate of change of current in an inductor? Answer guidance: V = L × (dI/dt).

2. Name three types of inductor cores and one advantage of each. Answer guidance: Air-core (no core losses, good for RF), iron-core (high inductance, low cost, good for low frequency), ferrite-core (low loss at high frequency, good for switching supplies).

Understanding

3. Why does an ideal inductor have zero voltage drop when carrying steady DC current? Answer guidance: Voltage across an inductor depends on the rate of change of current, dI/dt. Steady DC means current is not changing, so dI/dt = 0, giving V = 0.

4. Explain why opening a switch connected to an energized relay coil can produce a spark or damage nearby components. Answer guidance: The coil's magnetic field collapses suddenly when current is interrupted, inducing a large back-EMF as the inductor tries to maintain current flow. This voltage spike can arc across the switch contacts or exceed the breakdown voltage of a nearby transistor.

Application

5. A 10 mH inductor has a current that changes from 0 to 2 A in 5 ms. What voltage is induced across it during this change? Answer guidance: V = L × (dI/dt) = 0.01 × (2/0.005) = 0.01 × 400 = 4 V.

6. You are designing a switching power supply operating at 500 kHz and need to smooth pulsed current. Which core material would you choose and why? Answer guidance: Ferrite core — it has high permeability with low eddy-current losses at high switching frequencies, unlike iron, which would overheat from core losses at 500 kHz.

Analysis

7. An LC circuit has L = 10 µH and C = 100 pF. Calculate the resonant frequency and explain what happens to circuit impedance at that frequency in a series LC circuit. Answer guidance: f₀ = 1/(2π√(LC)) = 1/(2π√(10×10⁻⁶ × 100×10⁻¹²)) ≈ 5.03 MHz. At resonance in a series LC circuit, the inductive and capacitive reactances cancel, so impedance drops to its minimum (just the resistance), maximizing current.

8. Compare what happens to inductive reactance and capacitive reactance as frequency increases, and explain why this makes LC combinations useful for filters. Answer guidance: Inductive reactance X_L = 2πfL increases with frequency; capacitive reactance X_C = 1/(2πfC) decreases with frequency. Combining them lets a filter pass one frequency range while blocking another — e.g., an inductor blocks high frequencies while a capacitor shunts them to ground, reinforcing the low-pass effect.

FAQ

Why do transformers use inductors instead of some other component? A transformer relies on two inductors (windings) sharing a common magnetic core. Current changing in the primary winding creates a changing magnetic field, which induces a voltage in the secondary winding — this mutual inductance is exactly the mechanism that lets transformers step voltage up or down while providing electrical isolation between circuits.

What does the henry actually represent? One henry means that a current changing at a rate of one ampere per second induces one volt across the inductor. It's a fairly large unit for most electronics — real-world inductors used in signal and power circuits usually range from a few microhenries to a few hundred millihenries.

Why do inductors hum or buzz sometimes? Audible humming, especially in mains transformers, is usually caused by magnetostriction — the core material physically expanding and contracting slightly as the magnetic field alternates at 50/60 Hz — or by loose windings vibrating. It's mostly a mechanical, not electrical, issue.

Can an inductor store energy indefinitely like a charged capacitor? No. An inductor only stores energy while current is actively flowing through it; if current stops, the magnetic field collapses and the energy is released (often as that flyback voltage spike) rather than sitting stored the way a charged capacitor holds its charge.

Why are air-core inductors used in RF circuits instead of iron or ferrite cores? At radio frequencies, magnetic core materials introduce losses (hysteresis and eddy currents) that would waste signal energy and distort the response. Air has no such losses, so despite giving lower inductance for the same coil size, air-core inductors preserve signal quality better at high frequencies.

Quick Revision

• An inductor stores energy in a magnetic field created by current flow
• V = L(dI/dt): voltage depends on the rate of change of current, not current itself
• An ideal inductor has zero voltage drop under steady DC
• Inductive reactance X_L = 2πfL increases with frequency
• Energy stored: E = ½LI²
• Sudden current interruption causes a flyback voltage spike — use a flyback diode for protection
• Air-core: low inductance, no core loss, good for RF
• Iron-core: high inductance, good for low-frequency power, lossy at high frequency
• Ferrite-core: good balance for high-frequency switching supplies
• Toroidal cores minimize field leakage and interference
• LC resonant frequency: f₀ = 1/(2π√(LC))
• Series inductors add: Ltotal = L1 + L2; parallel inductors combine as 1/Ltotal = 1/L1 + 1/L2

Related Topics

Prerequisites: Electromagnetism basics; Faraday's law; Ohm's law; capacitors (for contrast)

Related Topics: Capacitors (LC resonant circuits, filters); transformers; diodes (flyback protection); oscillator circuits

Next Topics: Diodes; transformer design; LC filter design; switching power supply topologies