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Courses/Electrical Fundamentals/Power & Energy

lesson · 8min · Lesson 22 of 37

Efficiency and power loss in cables

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 · 8min
POWER TRIANGLEφP: real (W)Q (VAr)S (VA)PF = P / S= cos φS² = P² + Q²
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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

Efficiency and power loss in cables

Electrical Fundamentals · Lesson 22 · Beginner

BeginnerReview: professional review pending

Purpose

Quantify useful efficiency and resistive cable loss while avoiding false design approval.

Before you beginPower · Resistance · Current

Learning objectives

  • Calculate I²R loss
  • Calculate efficiency
  • Relate loss to voltage drop
  • Explain why current strongly affects heating

Real systems lose part of their input energy. In conductors, resistance produces heating that grows with the square of current.

CABLE LOSS AND EFFICIENCYCABLE LOSS AND EFFICIENCYinputoutputPloss = I²Rη = Pout / Pin

Core theory

Conductor loss is Ploss=I²R; doubling current at the same resistance quadruples loss.

Voltage drop across the conductor is IR, and Ploss also equals I times that drop.

Efficiency is useful output divided by input. The missing power becomes heat, sound, magnetic loss, or another non-useful form.

Terms, symbols, and units
TermMeaningSymbolUnit
Power lossInput power not delivered as useful outputPlossW
EfficiencyUseful output power divided by input powerηratio or %
Voltage dropPotential difference caused by path impedanceVdV
Ploss=I²R=I·Vd; η=Pout/Pin

Use total path resistance at the relevant operating temperature.

W and %
Worked exampleA two-conductor path has total resistance 0.40 Ω and carries 10 A to a 230 V load.

Assumptions: Resistance is the full outgoing and return path at operating temperature.

  1. Drop: Vd = 10 × 0.40 = 4 V.
  2. Loss: Ploss = 10² × 0.40 = 40 W.
  3. Check: I·Vd = 10 × 4 = 40 W.

Cable drop is 4 V and loss is 40 W.

Reasonableness check: The two independent loss forms agree.

Common mistakes
  • Using one-way resistance only
  • Using cold resistance for a hot operating condition without qualification
  • Calling an efficient result a compliant cable design

Where this appears in practice

Loss analysis informs cable sizing, low-voltage systems, feeders, batteries, and energy-efficiency work.

SafetyPersistent conductor or termination heating can cause fire. Cable selection requires current capacity, voltage drop, fault withstand, installation method, ambient conditions, and protection, not I²R alone.
Local code checkThese analysis laws are universal. Installation design, conductor selection, protection, testing, and permitted work must follow current local standards and manufacturer data.

Knowledge check

If current doubles with resistance unchanged, how does cable loss change?

It becomes four times larger. Loss is proportional to current squared.

Answer: It becomes four times larger. Loss is proportional to current squared.

Practical exercise

Compare loss at 5 A and 15 A through 0.2 Ω, then explain why the current ratio and loss ratio differ.

Summary

  • Conductor loss follows I²R
  • Voltage drop and loss are linked
  • Efficiency is output divided by input

Sources and review

  • University Physics Volume 2: Kirchhoff's Rules: OpenStax; Current web edition; Physics reference
  • SI Units: Electric Current: NIST; Current web edition; United States / SI 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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