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Courses/Electrical Fundamentals/Capacitors & Inductors

lesson · 10min · Lesson 32 of 37

Inductors in AC circuits: reactance

Course syllabusCourse overview
01Atoms, Electrons & Electric Charge
  1. ReadWhat is electricity?: atomic model
  2. ReadElectric charge and the coulomb
  3. ReadConductors, insulators, and semiconductors
  4. ReadConventional current vs electron flow
  5. quizModule quiz
02Voltage, Current & Resistance
  1. ReadPotential difference: the driving force
  2. ReadCurrent: the rate of charge flow
  3. ReadResistance and resistivity
  4. ReadOhm's Law: derivation and examples
  5. exerciseWorked examples: Ohm's Law problems
03Series & Parallel Circuits
  1. ReadSeries circuits: characteristics and rules
  2. ReadParallel circuits: characteristics and rules
  3. ReadCombined series-parallel networks
  4. ReadVoltage dividers and current dividers
  5. exerciseCircuit analysis practice
04Kirchhoff's Laws
  1. ReadKCL: Kirchhoff's Current Law
  2. ReadKVL: Kirchhoff's Voltage Law
  3. ReadMesh and nodal analysis
  4. exerciseKirchhoff's law problems set
05Power & Energy
  1. ReadElectrical power: watts and horsepower
  2. ReadEnergy: kilowatt-hours and joules
  3. ReadEfficiency and power loss in cables
  4. quizPower quiz
06Alternating Current Fundamentals
  1. ReadAC vs DC: why AC won
  2. ReadSinusoidal waveforms: peak, RMS, average
  3. ReadFrequency and period
  4. ReadPhase relationships
  5. ReadAC circuit analysis introduction
07Capacitors & Inductors
  1. ReadCapacitor construction and capacitance
  2. ReadCapacitors in AC circuits: reactance
  3. ReadInductor construction and inductance
  4. ReadInductors in AC circuits: reactance
  5. ReadRC and RL circuits: time constants
08Measurement & Instruments
  1. ReadMultimeters: AC/DC voltage and current
  2. ReadClamp meters and measuring live current
  3. ReadOscilloscopes: reading waveforms
  4. quizFinal assessment
Lesson · 10min
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In this lesson

PurposeCore theoryWorked exampleKnowledge checkSources

In this lesson

PurposeCore theoryWorked exampleKnowledge checkSources
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ElectraCore lesson handout

Inductors in AC circuits: reactance

Electrical Fundamentals · Lesson 32 · Beginner

BeginnerReview: professional review pending

Purpose

Calculate inductive reactance and explain why inductor current lags voltage in sinusoidal operation.

Before you beginInductance · Frequency · Phase

Learning objectives

  • Use XL formula
  • Predict frequency effect
  • State current lag
  • Separate reactance from winding resistance

An ideal inductor's opposition grows with frequency because faster current change induces greater voltage.

INDUCTIVE REACTANCEINDUCTIVE REACTANCE XL = 2πfLstored energy and time-dependent response

Core theory

XL=2πfL, so reactance rises directly with frequency and inductance.

For an ideal inductor, current lags voltage by 90°.

A practical coil impedance includes winding resistance and core effects, not XL alone.

Terms, symbols, and units
TermMeaningSymbolUnit
Inductive reactanceMagnitude opposition of ideal inductorXLΩ
Lagging currentCurrent reaches corresponding phase laterNot applicableNot applicable
Coil impedanceCombined winding resistance and reactanceZΩ
XL=2πfL; I=V/XL

Ideal sinusoidal steady-state relationship.

Ω, Hz, H, A
Worked exampleA 0.10 H ideal inductor is connected to 24 V RMS at 50 Hz.

Assumptions: Sinusoidal source; Negligible winding resistance.

  1. Reactance: XL=2π×50×0.10=31.42 Ω.
  2. Current: I=24/31.42=0.764 A RMS.
  3. Phase: Current lags voltage by 90°.

XL≈31.4 Ω and I≈0.764 A RMS lagging.

Reasonableness check: The magnitude acts like 31.4 Ω in I=V/X, but it is not heat-producing resistance.

Common mistakes
  • Using the capacitive reciprocal formula
  • Saying current leads
  • Ignoring winding resistance

Where this appears in practice

Inductive reactance shapes motor, transformer, choke, solenoid, and filter currents.

SafetyCoils can overheat, saturate, and generate switching transients. Confirm frequency, voltage, duty, temperature, and suppression ratings.
Local code checkThe component relationships are universal. Product ratings, discharge provisions, protective measures, permitted work, and test procedures must follow current local rules and manufacturer data.

Knowledge check

What happens to XL when frequency doubles?

It doubles. XL is directly proportional to frequency.

Answer: It doubles. XL is directly proportional to frequency.

Practical exercise

Calculate XL for 20 mH at 50 Hz and 500 Hz and compare currents at fixed voltage.

Summary

  • XL rises with f and L
  • Inductor current lags
  • Real coil impedance includes resistance

Sources and review

  • University Physics Volume 2: Capacitance, Inductance, and AC Circuits: OpenStax; Current web edition; Physics reference
  • The International System of Units (SI Brochure): BIPM; 9th edition, updated 2026; International

Editorial review date: 2026-08-21. Professional electrical review is pending.

Educational material for learning and preliminary checks. Verify current local requirements and exact equipment instructions. This lesson does not replace competent professional work.

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