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Ohm's Law

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Electric Current and ResistanceOhm's Law: V = IR+1 more→→Circuit Topology and Basic Circuit ElementsCircuit Variables and Ideal Circuit Elements+4 more
ohms-law voltage current resistance circuits

Core Idea

Ohm's law states that for many conducting materials (ohmic materials), the current through a device is proportional to the voltage across it: V = IR. The constant of proportionality R is the resistance, measured in ohms (Ω = V/A). Ohm's law is an empirical relationship, not a fundamental law — it holds for metals over a wide temperature range but breaks down for semiconductors, diodes, and other nonlinear devices.

How It's Best Learned

Verify Ohm's law experimentally (or through simulation) by plotting V vs. I for resistors — a straight line through the origin with slope R. Then identify non-ohmic devices (LEDs, diodes) where V-I curves are nonlinear.

Common Misconceptions

Explainer

You already know that current is the flow of charge and that resistance is opposition to that flow. Ohm's law, V = IR, says that in many materials these three quantities are locked in a simple linear relationship: double the voltage, double the current; double the resistance, halve the current. The law is deceptively simple in form but its implications ripple through every circuit you will ever analyze.

The causal direction matters. Voltage (potential difference, maintained by a battery or power supply) *drives* current through a resistance. Writing R = V/I is a *definition* of resistance from a measurement — apply V, measure I, compute R — not a statement that resistance is caused by voltage. For an ohmic material like a metal resistor, R is a constant property of the material and geometry, independent of what V or I you choose. This constancy is what it means to be ohmic: the V-I graph is a straight line through the origin, with slope equal to resistance.

The microscopic picture behind Ohm's law helps explain where it comes from and why it fails. In a metal, free electrons constantly scatter off vibrating ions. Voltage accelerates electrons between collisions, but collisions constantly reset their drift velocity. The result is a steady average drift speed proportional to the applied field — and therefore a current proportional to voltage. Temperature matters because hotter ions vibrate more, causing more frequent collisions and higher resistance. This is why real resistors heat up and why the resistance of incandescent bulbs changes dramatically from cold to operating temperature.

Ohm's law fails for many important devices. A diode conducts almost no current until voltage exceeds a threshold, then conducts heavily — its V-I curve is exponential, not linear. A transistor uses a small control signal to modulate a large current. Neither is well described by a single fixed resistance. The word "non-ohmic" is not a flaw — diodes and transistors are precisely useful *because* they violate Ohm's law. Understanding where Ohm's law applies (metal resistors, over a limited temperature range) versus where it breaks down (semiconductor devices, plasmas, superconductors) is essential for working with real circuits.

Practice Questions 5 questions

Prerequisite Chain

Understanding Zero → The Number Zero → Counting to Five → Counting to 10 → Counting to 20 → Counting a Set of Objects Up to 20 → Cardinality: The Last Number Counted → Matching Numerals to Quantities → Subitizing Small Quantities → Addition Within 10 → Number Bonds to 10 → Addition Within 20 → Doubles and Near Doubles → Doubles Facts Within 10 → Near Doubles Facts Within 20 → Mental Math Strategies for Addition → Mental Math: Adding and Subtracting Tens → Addition Within 100 → Repeated Addition as Multiplication → Multiplication as Equal Groups → Multiplication: Arrays → Basic Multiplication Facts (0s, 1s, 2s, 5s, 10s) → Multiplication Facts Within 100 → Division as Equal Sharing → Division as Grouping (Measurement Division) → Division: Grouping (Repeated Subtraction) Model → Division: Fair Sharing Model → Division as Equal Sharing → Division as Grouping → Basic Division Facts → Division Facts Within 100 → Multiplication and Division Fact Families → Relationship Between Multiplication and Division → Division Facts as Inverse of Multiplication → Remainders and Quotients in Division → Division Word Problems → Multi-Step Word Problems → Solving Multi-Step Word Problems → Multiplication Word Problems → Division Word Problems → Introduction to Long Division → Factors and Multiples → Prime and Composite Numbers → Equivalent Fractions → Relating Fractions and Decimals → Decimal Place Value → Integers and the Number Line → Comparing and Ordering Integers → Absolute Value → Adding Integers → Subtracting Integers → Multiplying Integers → Dividing Integers → Unit Rates → Proportions → Percent Concept → Converting Between Fractions, Decimals, and Percents → Operations with Rational Numbers → Two-Step Equations → Solving Multi-Step Equations → Equations with Variables on Both Sides → Angle Pairs: Complementary, Supplementary, and Vertical → Parallel Lines and Transversals → Corresponding Angles → Alternate Interior Angles → Triangle Angle Sum Theorem → Exterior Angle Theorem → Triangle Inequality Theorem → Similar Triangles: AA Similarity → Similar Triangles: SSS and SAS Similarity → Proportions in Similar Triangles → Right Triangle Trigonometry Introduction → Sine, Cosine, and Tangent Ratios → Trigonometric Ratios Review → Radian Measure → Converting Between Degrees and Radians → The Unit Circle → Graphing Sine and Cosine → Graphing Tangent and Reciprocal Trigonometric Functions → Derivatives of Trigonometric Functions → Antiderivatives → Indefinite Integrals → Basic Integration Rules → Riemann Sums → Definite Integral Definition → Double Integrals: Definition and Setup → Iterated Integrals and Fubini's Theorem → Double Integrals over Rectangular Regions → Double Integrals over General Regions → Applications of Double Integrals: Area, Mass, and Moments → Triple Integrals in Cartesian Coordinates → Triple Integrals in Cylindrical and Spherical Coordinates → Change of Variables and the Jacobian Determinant → Applications of Triple Integrals: Volume and Mass → Vector Fields and Their Representations → Line Integrals of Vector Fields → Conservative Vector Fields and Potential Functions → Electric Potential → Electric Current and Resistance → Ohm's Law

Longest path: 100 steps · 601 total prerequisite topics

Prerequisites (3)

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