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Courses/Electrical Fundamentals/Voltage, Current & Resistance

lesson · 12min · Lesson 9 of 37

Ohm's Law: derivation and examples

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 · 12min
VRΩAV = I × RI = V / RR = V / IP = V × I
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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

Ohm's Law: derivation and examples

Electrical Fundamentals · Lesson 9 · Beginner

BeginnerReview: professional review pending

Purpose

Apply Ohm's law with units, substitution, checks, and awareness of its limits.

Before you beginVoltage · Current · Resistance · Rearranging simple equations

Learning objectives

  • Use all three Ohm's-law forms
  • Show substitutions with units
  • Check answers by inverse calculation
  • Identify non-ohmic behavior

Ohm's law connects voltage, current, and resistance for a component when its physical conditions are sufficiently constant.

OHM'S LAW: ONE RELATIONSHIP, THREE FORMSOHM'S LAW: ONE RELATIONSHIP, THREE FORMS VIRV = I × RI = V ÷ R

Core theory

For an ohmic component at constant temperature, current is proportional to voltage and the ratio V/I is constant.

The three useful forms are V = IR, I = V/R, and R = V/I. Choose the form that leaves the required quantity alone.

Lamps, diodes, thermistors, motors, and many electronic loads are not described by one constant resistance across all operating points.

Terms, symbols, and units
TermMeaningSymbolUnit
OhmicHaving an approximately constant V/I ratio under stated conditionsNot applicableNot applicable
Operating pointThe specific voltage and current at which a device is workingNot applicableNot applicable
I–V characteristicGraph showing current response to applied voltageNot applicableNot applicable
V = I × R | I = V ÷ R | R = V ÷ I

Use volts, amperes, and ohms together; convert prefixes first.

V = A·Ω; A = V/Ω; Ω = V/A
Worked exampleA 24 V control supply feeds a 120 Ω coil. Calculate current and power.

Assumptions: The coil is represented as 120 Ω at this operating condition; Supply and conductor drop are neglected.

  1. Current formula: I = V/R.
  2. Current substitution: I = 24 V ÷ 120 Ω = 0.200 A.
  3. Power check: P = VI = 24 V × 0.200 A = 4.8 W.
  4. Inverse check: IR = 0.200 A × 120 Ω = 24 V.

Current is 0.200 A (200 mA); power is 4.8 W.

Reasonableness check: A resistance five times the voltage number gives one-fifth of an ampere; the inverse check returns the supply voltage.

Common mistakes
  • Entering milliamperes as amperes
  • Multiplying when the required form needs division
  • Applying a cold resistance to a hot filament or energized coil without qualification

Where this appears in practice

Ohm's law supports sensor-loop checks, coil-current estimates, resistor selection, and first-pass fault diagnosis.

SafetyA mathematically correct result does not prove a component, conductor, or power source is safe. Confirm ratings, temperature, fault energy, isolation, and protective measures.
Local code checkOhm's law is universal; installation permissions, conductor protection, testing, and live-work rules are local and task-specific.

Knowledge check

A 48 V circuit carries 0.40 A. What resistance does it present?

120 Ω. R = V/I = 48 V ÷ 0.40 A = 120 Ω.

Answer: 120 Ω. R = V/I = 48 V ÷ 0.40 A = 120 Ω.

Practical exercise

Choose a safe low-voltage resistor example, calculate expected current and power, then compare with a simulator or supervised bench measurement.

Summary

  • Choose the rearranged form for the unknown
  • Carry units through every step
  • Check with an inverse calculation
  • State when resistance may change

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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