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lesson · 10min · Lesson 30 of 37

Capacitors 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

Capacitors in AC circuits: reactance

Electrical Fundamentals · Lesson 30 · Beginner

BeginnerReview: professional review pending

Purpose

Calculate capacitive reactance and explain why capacitor current leads voltage in sinusoidal operation.

Before you beginCapacitance · Frequency · Phase

Learning objectives

  • Use XC formula
  • Predict frequency effect
  • State current lead
  • Recognise non-ideal limits

A capacitor resists change in voltage. Under sinusoidal excitation this produces frequency-dependent reactance rather than a fixed DC resistance.

CAPACITIVE REACTANCECAPACITIVE REACTANCE XC = 1/(2πfC)stored energy and time-dependent response

Core theory

XC=1/(2πfC), so higher frequency or capacitance lowers reactance.

For an ideal capacitor, current leads voltage by 90° because current is proportional to the rate of voltage change.

Real capacitors add equivalent series resistance, leakage, inductance, and ratings.

Terms, symbols, and units
TermMeaningSymbolUnit
Capacitive reactanceMagnitude opposition of ideal capacitorXCΩ
Leading currentCurrent reaches corresponding phase earlierNot applicableNot applicable
ESREquivalent series resistance representing lossNot applicableΩ
XC=1/(2πfC); I=V/XC

Applies to sinusoidal steady-state magnitudes.

Ω, Hz, F, A
Worked exampleFind reactance and current for 100 µF at 50 Hz on 24 V RMS.

Assumptions: Ideal capacitor; Sinusoidal source.

  1. Convert: C=100×10⁻⁶ F.
  2. Reactance: XC=1/(2π×50×100e−6)=31.83 Ω.
  3. Current: I=24/31.83=0.754 A RMS, leading.

XC≈31.8 Ω and I≈0.754 A RMS leading voltage.

Reasonableness check: A larger capacitance or frequency would yield more current.

Common mistakes
  • Multiplying instead of taking reciprocal
  • Using µF as F
  • Saying a capacitor dissipates reactive power as heat

Where this appears in practice

Capacitive reactance appears in filters, motor capacitors, coupling, and power-factor correction.

SafetyPower capacitors may carry substantial current and retain charge. Confirm discharge, fusing, voltage, ripple, and duty 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 XC if frequency doubles?

It halves. XC is inversely proportional to frequency.

Answer: It halves. XC is inversely proportional to frequency.

Practical exercise

Calculate XC for 10 µF at 50 Hz and 1 kHz, then compare.

Summary

  • XC falls as f or C rises
  • Capacitor current leads voltage
  • Real capacitors have loss and limits

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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