Inductive reactance

Resistance (R) limits current by dissipating energy as heat. Inductive reactance limits current by induced counter-voltage — no intentional heat in an ideal inductor.

Both are measured in ohms. In calculations you can substitute XL for R in Ohm's law when the circuit is purely inductive:

I = E / XL

Symbol: XL ("X sub L"). General reactance is X; inductive is XL; capacitive (later course) is XC.

Think of XL as dynamic opposition — it exists only while current is changing, which in AC is all the time.

XL = 2πfL

Where:

XL depends on two things you control or read from the nameplate:

1. Physical inductance L — turns, core material, core size, gap
2. Line frequency f — 60 Hz in most of North America; 50 Hz in much of Europe and Asia

Double the inductance → double XL. Double the frequency → double XL.

Induced voltage depends on how fast flux cuts the conductors. Higher frequency means the AC waveform completes more cycles per second — the field changes faster — more induced volts → higher XL.

Example from the book: an inductor at 60 Hz draws 24 A from 480 V (XL = 20 Ω). Same coil at 400 Hz:

• First find L: L = XL / (2πf) = 20 / 377 ≈ 0.053 H
• At 400 Hz: XL = 2π × 400 × 0.053 ≈ 133 Ω
• New current: I = 480 / 133 ≈ 3.6 A

Same coil, same voltage — frequency change dramatically changes current.

Field shortcut at 60 Hz:

2π × 60 ≈ 377

So: XL ≈ 377 × L and L ≈ XL / 377

Rearrange:

L = XL / (2πf)

Example: 36 V, 400 Hz, I = 0.2 A

1. XL = E / I = 36 / 0.2 = 180 Ω
2. L = 180 / (2π × 400) ≈ 0.0716 H

Example: 120 V, 60 Hz, coil 0.8 H, negligible wire R

1. XL = 2 × 3.1416 × 60 × 0.8 ≈ 301.6 Ω
2. I = 120 / 301.6 ≈ 0.398 A

Always find XL first when solving for current in a pure-L branch.

L is fixed by construction, not by the voltage you apply:

• More turns → more L
• Turns closer together → more L
• Iron or ferrite core → much more L than air
• Larger core cross-section → more L

Once the part is built, L is constant. Only f and XL change when you move it to another frequency.

Units: henry (H). Field values are often millihenries (mH).

For a pure inductive branch (Q high, wire R negligible):

When wire resistance matters (real motor coil, contactor), total opposition is impedance Z, not XL alone — covered in later lessons.

A 0.5 H choke at 120 V:

• At 60 Hz: XL = 377 × 0.5 ≈ 188.5 Ω → I ≈ 0.64 A
• At 50 Hz: XL = 314 × 0.5 ≈ 157 Ω → I ≈ 0.76 A

Running a 50 Hz rated choke on 60 Hz increases current roughly 20% — enough to overheat over time. Running 60 Hz equipment on 50 Hz usually lowers current but may affect saturation and performance — still a mismatch to avoid.

Situation. A 480 V, 60 Hz reactor nameplate is illegible. An identical unit on another line draws 18 A with 324 V measured across the reactor (rest of drop elsewhere). De-energized, ohmmeter reads 1.2 Ω wire resistance.

Steps.

1. XL ≈ E / I = 324 / 18 = 18 Ω (if R negligible — check Q later)
2. L = 18 / 377 ≈ 0.048 H order value
3. VAR rating ≈ E × I = 324 × 18 ≈ 5832 VAR minimum

Applied lesson. XL from running amps and volts gives you orderable inductance when the paint is gone — but verify wire R before assuming pure inductance.