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Courses/Electrical Fundamentals/Alternating Current Fundamentals

lesson · 13min · Lesson 28 of 37

AC circuit analysis introduction

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 · 13min
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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

AC circuit analysis introduction

Electrical Fundamentals · Lesson 28 · Beginner

BeginnerReview: professional review pending

Purpose

Introduce AC impedance and phasor relationships without treating reactance as energy dissipation.

Before you beginRMS values · Phase · Ohm's law

Learning objectives

  • Define impedance
  • Separate resistance and reactance
  • Use RMS phasor Ohm's law
  • Distinguish real and reactive behaviour

In sinusoidal steady state, impedance extends resistance by representing both magnitude opposition and phase shift.

AC IMPEDANCEAC IMPEDANCE Z = R + jX

Core theory

Resistance dissipates average power; ideal inductors and capacitors store energy temporarily and return it, producing reactance.

Impedance Z is complex: Z=R+jX. Its magnitude relates RMS voltage and current, while its angle gives phase.

For series RLC, X=XL−XC and |Z|=√(R²+X²).

Terms, symbols, and units
TermMeaningSymbolUnit
ImpedanceComplex voltage-to-current ratioZΩ
ReactanceFrequency-dependent energy-storage oppositionXΩ
PhasorComplex representation of a sinusoid at one frequencyNot applicableNot applicable
V=IZ; |Z|=√(R²+X²)

Phasor quantities use one common sinusoidal frequency and normally RMS magnitudes.

V, A, Ω
Worked exampleA series load has R=30 Ω and net inductive reactance X=40 Ω on 100 V RMS.

Assumptions: Sinusoidal steady state.

  1. Magnitude: |Z|=√(30²+40²)=50 Ω.
  2. Current: I=100/50=2 A RMS.
  3. Angle: φ=atan(40/30)=53.1°, so current lags.

|Z|=50 Ω; I=2 A RMS; current lags by about 53°.

Reasonableness check: The 3-4-5 triangle makes impedance exceed both components.

Common mistakes
  • Adding R and X arithmetically
  • Calling reactance consumed power
  • Mixing peak voltage with RMS current

Where this appears in practice

Impedance underpins AC loads, filters, motors, transformers, power factor, and fault calculations.

SafetyA small measured DC resistance does not imply small AC impedance, and stored energy may remain after isolation. Follow discharge and verification procedures.
Local code checkThe physics and SI relationships are universal. Nominal frequency, supply characteristics, permitted work, and instrument requirements must be confirmed for the actual jurisdiction and task.

Knowledge check

For a purely resistive AC load, what is the voltage-current phase angle?

0°. Resistor voltage and current are in phase.

Answer: 0°. Resistor voltage and current are in phase.

Practical exercise

Find impedance magnitude and current for R=12 Ω, X=5 Ω at 26 V RMS.

Summary

  • Impedance includes resistance and reactance
  • Reactance shifts phase
  • Use consistent RMS phasors

Sources and review

  • University Physics Volume 2: Alternating-Current 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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