Inside the inductor
A coil of wire: the capacitor’s twin, storing energy in a magnetic field instead of an electric one. Inductors smooth current, filter noise, tune radios, and are the heart of every switching power supply. And they bite: switched off, an inductor fights back with a voltage spike. Every picture below is computed while you watch.
What it is
Current through a wire makes a magnetic field around it. Wind the wire into a coil and the fields of the turns add up; wind it on a magnetic core and the core multiplies the field hundreds or thousands of times. Change the current and the changing field induces a voltage in the coil itself that opposes the change (Faraday and Lenz): that self-induced voltage is inductance.
v = L · di/dt L = µ0 · µr · N² · A / l U = ½ · L · I²
L in henries grows with the square of the turns N and with the core’s permeability µr, and with the coil’s area A over its length l; µ0 = 4π × 10⁻⁷ H/m. A capacitor resists a change of voltage; an inductor resists a change of current.
How it’s made
How it works: the magnetic field
A side section through the coil: each turn crosses the page twice, coming out on top (⊙) and going in at the bottom (⊗). The field lines are traced from those currents (Biot–Savart). Inside the coil the fields of the turns add up; outside, they close back around like a bar magnet’s. Reverse the current and the poles swap.
The coil: 10 mm across, 30 mm long. Up to 16 turns are drawn; the numbers use all of them. A closed core is drawn as a loop with the winding on one leg: the flux stays inside it.
Switching it on and off: back-EMF and the spike
Switched on, the current cannot jump: it rises along i = (V/R)(1 − e^(−t·R/L)), with τ = L/R, while the field builds. Switched off, the field collapses and the coil does everything it can to keep the current flowing: its voltage reverses and climbs until the current finds a path. With nothing but the switch’s own few picofarads, that is hundreds or thousands of volts. This is why every relay, solenoid and motor driver needs a flyback diode.
Switch on, wait, switch off. The spike is too fast to draw on the same time scale (nanoseconds to microseconds), so its peak is computed: V + I·√(L/C) with the switch’s 100 pF. The chart’s time is stretched so one τ takes 2.5 s.
The core: saturation and the air gap
A magnetic core multiplies the field only up to a point. Its flux density B follows the magnetising force H until the core’s domains are all lined up: past that saturation flux (about 0.4 T for ferrite, 1.5–1.8 T for silicon steel) the core adds nothing more and the inductance collapses. The loop’s width is hysteresis: energy lost as heat each cycle. Power inductors and flyback transformers have a small air gap: it lowers the inductance but lets the core take far more current before saturating.
20 turns on a ferrite core (path 50 mm, area 0.5 cm², µr 2 300, Bsat 0.38 T). The hysteresis loop is widened so you can see it. On the right: the current in the inductor of a converter with 5 V across it for 10 µs at a time, starting from the DC current you set.
With AC: reactance and the 90° lag
On AC an inductor opposes the current more the faster it alternates: XL = 2π f L. That is the mirror image of a capacitor, and it is how inductors choke off high-frequency noise while passing DC and low frequencies. The current lags the voltage by a quarter cycle.
What goes wrong
- The switch-off spike kills transistors and burns relay contacts (the arc you see when you unplug a running motor). The fixes: a flyback diode, a snubber (RC), a TVS, or a MOSFET rated for avalanche.
- Saturation: run a power inductor past its rated current and the current spikes each cycle; the switch overheats and the converter may fail. Choose by saturation current, not just inductance.
- Heat: copper loss (I²R in the winding) and core loss (hysteresis and eddy currents, rising with frequency). Ferrite loses permeability near its Curie temperature, around 200 °C.
- Noise and coupling: an open coil’s field spreads and couples into neighbours. Shielded and toroidal parts keep it in.
From inductor to transformer
Put a second winding on the same core and the changing flux of the first induces a voltage in the second: a transformer. The voltage per turn is the same in both windings, so the turns ratio sets the voltage. It is the reason the grid uses AC, and inside every phone charger there is a tiny one switching at 100 kHz.
Use it on the bench
Every lesson below opens in the lab with a real circuit: the same physics, now with a meter and a scope.
- RL transient — watch the current rise along 1 − e^(−t·R/L) (about it)
- Inductive load and the flyback diode — an inductive load, the spike, and the diode that stops it (about it)
- RLC series circuit — an inductor and a capacitor resonating (about it)
- Buck converter from parts — a buck converter built from parts: the inductor at work (about it)
- Boost converter from parts — a boost converter: the inductor’s energy lifting the voltage (about it)
- Basic transformer — a transformer stepping 230 V down (about it)
Check yourself
Exam-style questions (ECE, EE and NC-II reviewers ask these). Each answer links to the scene that shows it.
1. A coil’s number of turns is doubled, same core and size. Its inductance:
L = µ0·µ·N²·A/l: inductance grows with the square of the turns. Try the turns slider in the field scene. See the scene ▸
2. A 100 mH coil with 50 Ω of winding resistance is switched onto 12 V. The time constant and the final current are:
τ = L/R = 0.1/50 = 2 ms; the current settles at V/R = 12/50 = 240 mA. Like a capacitor charging, it reaches 63 % after one τ. See the scene ▸
3. A relay coil is switched off by a transistor with no diode across it. What happens?
v = L·di/dt: stopping the current instantly would need an infinite voltage. The spike climbs until something breaks down, often the transistor. Try it in the switching scene with the BJT. See the scene ▸
4. What does a flyback diode across a relay coil do?
The diode is reverse-biased while the switch is on. When it opens, the current circulates through the diode and dies away in the coil’s resistance. The relay releases a little slower. See the scene ▸
5. The energy stored in a 2 mH inductor carrying 3 A is:
U = ½·L·I² = 0.5 × 0.002 × 9 = 9 mJ. This energy is what a flyback converter moves each cycle, and what the spike dumps into a switch. See the scene ▸
6. Why do power-inductor cores often have an air gap?
The gap holds most of the magnetic “pressure” (H), so the ferrite reaches its saturation flux at a much higher current. Lower µ effective, lower L, but a usable current. Move the gap slider in the core scene. See the scene ▸
7. An inductor runs past its saturation current in a buck converter. The current:
di/dt = V/L: as L falls in saturation, the same voltage drives the current up much faster, stressing the switch and the inductor. See the scene ▸
8. A 10 mH inductor at 1 kHz has a reactance of about:
XL = 2πfL = 2π × 1 000 × 0.01 ≈ 63 Ω. Ten times the frequency, ten times the reactance: the opposite of a capacitor. See the scene ▸
9. In an inductor on AC, the current:
v = L·di/dt: the voltage is greatest where the current changes fastest, a quarter cycle before the current peaks. “ELI the ICE man”: in L, E (voltage) comes before I. See the scene ▸
10. Why is a ferrite rod antenna’s inductance far lower than the ferrite’s µr (about 2 000) would suggest?
Only a closed magnetic path (a toroid, an E-core) gets the material’s full permeability; an open rod gets an effective µ of tens. Compare the rod and the toroid in the field scene. See the scene ▸
Inside the other parts
The capacitor · the transformer · the resistor · the diode and LED · the transistor · the battery · all the parts