Inductance
What you’ll learn
- What an inductor is, and the one thing it does: oppose a change in current.
- The henry, and what makes a coil’s inductance bigger or smaller.
- The L/R time constant — how fast current builds in a coil on DC.
- Why current lags voltage by 90° in a pure inductance on AC.
- Inductive kick: the voltage spike when you open a circuit with a coil in it.
An inductor is a coil of wire, and it has one habit: it opposes any change in the current flowing through it. Switch it on and the current climbs gradually instead of jumping; switch it off and the coil tries to keep the current going. On AC, where the current never stops changing, that habit turns into a steady opposition to flow — and it pulls the current a quarter-cycle behind the voltage.
Why a coil pushes back
Current through a wire makes a magnetic field around it. Wind the wire into a coil and the fields of all the turns add up into one strong field through the middle. When the current changes, that field changes — and a changing magnetic field through a coil induces a voltage in it. The induced voltage always pushes against the change that made it (that is Lenz’s law). Rising current meets a voltage that tries to hold it down; falling current meets one that tries to hold it up.
How strongly a coil does this is its inductance, L, measured in henries (H). More turns, an iron core, a bigger cross-section and a shorter coil all mean more inductance. Pull the iron out of a coil and its inductance falls a long way.
On DC: the time constant
Close a switch to put DC across a coil and resistor, and the current does not jump straight to V ÷ R. It rises along a curve — fast at first, then slower and slower as it gets close. How long that takes is set by the time constant, τ (the Greek letter tau):
- τ = L ÷ Rseconds = henries ÷ ohms
- 1τ → 63.2%of the final current
- 5τ → 99.3%treated as “fully there”
Worked: a DC relay coil
- A 24 V DC coil has 0.5 H of inductance and 100 Ω of resistance.
- Final current = V ÷ R = 24 ÷ 100 = 0.24 A (240 mA).
- τ = L ÷ R = 0.5 ÷ 100 = 5 ms.
- After 1τ (5 ms): 0.632 × 0.24 = 0.152 A. After 5τ (25 ms) it is essentially the full 0.24 A.
Opening the circuit: inductive kick
The coil’s field holds energy. Open the switch and the current is asked to drop to zero instantly. The collapsing field induces whatever voltage it takes to keep the current flowing a moment longer — often many times the supply voltage. That is the spark you see at a switch or contact opening on a coil, and it is what destroys transistors and PLC outputs if the coil has no suppression. On DC coils the fix is a diode across the coil (reverse-biased in normal running) that gives the current a harmless loop to die away in.
On AC: current lags voltage
On AC the current is always changing, so the coil is always pushing back. In a pure inductance the result is that the current peaks a quarter-cycle — 90° — after the voltage. The opposition itself is called inductive reactance, XL, measured in ohms; it grows with frequency, and the reactance lesson works it out.
Coils in series and parallel
As long as their fields do not link each other, inductors combine just like resistors: in series they add (LT = L1 + L2 + …), in parallel they combine by reciprocals (1 ÷ LT = 1 ÷ L1 + 1 ÷ L2 + …). Two 20 mH coils: 40 mH in series, 10 mH in parallel.
Try one: a 2 H coil with 40 Ω of resistance on 120 V DC
Final current 120 ÷ 40 = 3 A. τ = 2 ÷ 40 = 0.05 s = 50 ms. It is essentially at 3 A after 5τ = 250 ms. (And a coil made for AC would usually cook on DC — its reactance is what normally holds the current down.)
Sur le chantier
Tips from the job
- Contactor coils, relay coils, solenoids, motor windings, transformers and ballasts are all inductors. Most of what you control on the job is a coil.
- An AC contactor coil pulls a big inrush the instant it is energized (the open magnetic gap means low inductance), then settles once the armature closes. A coil that buzzes or cooks has often failed to seal fully.
- DC coils on control circuits get a diode or a suppressor across them. If you replace one, put it back the same way round — a reversed diode shorts the supply.
- Treat a motor or transformer winding you have just opened as if it can still bite. Meter it before you touch the leads.
Common mistakes
- Expecting a coil to limit DC current. On steady DC only the wire resistance does — which is why an AC coil on DC burns out.
- Swapping “lags” and “leads”. Remember ELI: E before I in an inductor.
- Forgetting that the time constant is L ÷ R, not L × R.
- Removing a coil’s suppression diode because “it works without it”. It works until the kick kills the switching transistor.
Check yourself
8 questions. Tap an answer — it is marked straight away and the reason opens under it. Get 80% or better and the lesson is ticked off on the year page.
Not started yet.
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What does an inductor oppose?
Answer and why
B. A steady DC current through a coil is limited only by the wire’s resistance. What a coil fights is change — rising or falling current.
-
What is the unit of inductance?
Answer and why
C. Inductance is measured in henries (H). Small coils are in millihenries (mH) or microhenries (µH).
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A 0.5 H coil with 100 Ω of resistance is switched onto DC. What is its time constant?
Answer and why
B. τ = L ÷ R = 0.5 ÷ 100 = 0.005 s = 5 ms.
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After ONE time constant, the current in an RL circuit has reached about what share of its final value?
Answer and why
B. After 1τ it is 63.2%; after 5τ it is 99.3%, which is treated as “there”.
-
In a pure inductance on AC, the current…
Answer and why
C. ELI: in an inductor (L) the voltage (E) comes before the current (I). Current lags by a quarter cycle.
-
Why can opening a switch on a DC relay coil make a spark or damage electronics?
Answer and why
B. Stop the current suddenly and the coil’s field collapses, inducing a large voltage that tries to keep the current flowing. That is the inductive kick — hence suppression diodes and snubbers across coils.
-
Which change increases a coil’s inductance?
Answer and why
C. Inductance rises with the number of turns (roughly with turns squared) and with an iron core, which concentrates the magnetic field.
-
Two 20 mH coils in series, far apart so their fields don’t interact. Total inductance?
Answer and why
C. Inductors add in series like resistors: 20 + 20 = 40 mH. In parallel they combine like parallel resistors: 10 mH.
Questions fréquentes
What is self-inductance?
The current in a coil makes a magnetic field; when that current changes, the changing field induces a voltage back in the same coil, pushing against the change. That back-voltage is self-induction, and a coil’s inductance says how strong it is.
Why does an AC contactor coil burn out if it is put on DC of the same voltage?
On AC the coil’s inductive reactance limits the current far more than its wire resistance does. On DC there is no reactance — only the resistance — so the coil draws many times its rated current and overheats.
Voir aussi
- AC fundamentals — the lesson before this one.
- Capacitance — the coil’s opposite number.
- Reactance and impedance
- Contactor wiring diagram — the coil you will wire most often.
- Transformer basics — two coils sharing one field.
- All second year lessons
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