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Courses/Electrical Fundamentals/Alternating Current Fundamentals

lesson · 10min · Lesson 27 of 37

Phase relationships

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

Phase relationships

Electrical Fundamentals · Lesson 27 · Beginner

BeginnerReview: professional review pending

Purpose

Describe phase difference between equal-frequency sinusoids using time, degrees, and radians.

Before you beginSine waves · Period · Angles

Learning objectives

  • Define phase difference
  • Convert time shift to degrees
  • Identify lead and lag
  • Avoid comparing phase at different frequencies

Phase states where one periodic waveform is in its cycle relative to another waveform of the same frequency.

PHASE RELATIONSHIPSPHASE RELATIONSHIPS φ = 360°·Δt/T

Core theory

One full cycle equals 360° or 2π radians. A quarter-cycle shift is 90°.

A waveform leads if it reaches the same reference point earlier in time; it lags if later.

A fixed phase relationship is meaningful for signals of the same frequency; otherwise their relative phase changes with time.

Terms, symbols, and units
TermMeaningSymbolUnit
PhasePosition within a periodic cycleφ° or rad
LeadReach a reference point earlierNot applicableNot applicable
LagReach a reference point laterNot applicableNot applicable
φ=360°·Δt/T = 2π·Δt/T

Use a signed time shift and declare which signal is the reference.

degrees or radians
Worked exampleAt 50 Hz, current reaches its positive peak 5 ms after voltage.

Assumptions: Equal-frequency sinusoids.

  1. Period: T=20 ms.
  2. Fraction: Δt/T=5/20=0.25.
  3. Phase: 0.25×360°=90°; current lags voltage.

Current lags voltage by 90°.

Reasonableness check: Five milliseconds is one quarter of a 20 ms cycle.

Common mistakes
  • Reversing lead and lag
  • Using peak-to-peak time as period
  • Assigning fixed phase to unequal frequencies

Where this appears in practice

Phase matters in impedance, power factor, motors, transformers, filters, and signal timing.

SafetyPhase-to-phase measurement can expose the instrument to a much higher potential than phase-to-neutral. Use a method and probe system rated for the circuit.
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

A shift of half a cycle equals what phase angle?

180° or π radians. One full cycle is 360°.

Answer: 180° or π radians. One full cycle is 360°.

Practical exercise

Sketch two same-frequency waves with a 60° shift and label clearly which one leads.

Summary

  • Phase compares cycle position
  • Lead means earlier
  • Time shift converts through the period

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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