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Courses/Electrical Fundamentals/Voltage, Current & Resistance

lesson · 9min · Lesson 8 of 37

Resistance and resistivity

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 · 9min
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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

Resistance and resistivity

Electrical Fundamentals · Lesson 8 · Beginner

BeginnerReview: professional review pending

Purpose

Relate resistance to material, geometry, and temperature without treating resistance as a fixed property of every component.

Before you beginVoltage and current · Area and length

Learning objectives

  • Define resistance and resistivity
  • Use R = ρL/A
  • Predict effects of length and area
  • Recognise temperature dependence

Resistance describes how strongly a component opposes current at a stated condition. Resistivity is a material property; geometry turns that property into a conductor resistance.

RESISTANCE: MATERIAL + GEOMETRYRESISTANCE: MATERIAL + GEOMETRY longer → more Rlarger area → less RR = ρL ÷ A

Core theory

For a uniform conductor, resistance increases with length and decreases as cross-sectional area increases.

Resistivity depends on material and temperature. Copper has low resistivity, while insulation materials have extremely high resistivity.

Metallic conductor resistance normally rises with temperature, so design and test values must state or account for temperature.

Terms, symbols, and units
TermMeaningSymbolUnit
ResistanceRatio of voltage to current for the stated conditionRohm (Ω)
ResistivityMaterial property relating geometry to resistanceρΩ·m
Cross-sectional areaConductor area perpendicular to current flowAm² or mm² with matched ρ units
R = ρL ÷ A

Multiply resistivity by conductor length, then divide by cross-sectional area.

Use one consistent length/area system; Ω·m requires m and m².
Worked exampleA uniform wire is replaced with the same material and length but twice the cross-sectional area. What happens to resistance?

Assumptions: Temperature and material are unchanged; Connections are ignored.

  1. Original: R₁ = ρL/A.
  2. New area: R₂ = ρL/(2A).
  3. Compare: R₂/R₁ = 1/2.

Resistance is halved.

Reasonableness check: Twice the conducting area provides twice as much parallel path for charge movement.

Common mistakes
  • Mixing mm² with resistivity stated in Ω·m
  • Ignoring both outgoing and return conductor length
  • Assuming resistance is unchanged as a conductor heats

Where this appears in practice

Cable voltage drop and fault-loop calculations depend on conductor resistance, length, cross-section, material, and operating temperature.

SafetyUnexpected resistance at a loose termination produces local heating because loss is proportional to I²R. Discolouration or heat damage requires isolation and competent investigation.
Local code checkCable tables and temperature corrections are jurisdiction- and product-specific. Use current manufacturer data and applicable installation standards.

Knowledge check

If conductor length doubles while material and area stay constant, what happens to resistance?

It doubles. R is directly proportional to L in R = ρL/A.

Answer: It doubles. R is directly proportional to L in R = ρL/A.

Practical exercise

Compare the expected relative resistance of equal-length 1.5 mm² and 2.5 mm² conductors without using tabulated resistivity.

Summary

  • Resistance belongs to a component at stated conditions
  • Resistivity belongs to the material
  • Longer is higher resistance; larger area is lower

Sources and review

  • The Feynman Lectures on Physics, Volume II: Caltech; Online edition; Physics reference
  • International Electrotechnical Vocabulary: Electromagnetism: IEC; Current edition must be confirmed; International

Editorial review date: 2026-08-14. 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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