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Lesson 8.2 • Competency 8.1Complete Lesson
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Resistance, Resistivity & Temperature

Ohm’s law V = IR, resistance geometry R = ρl/A, electrical conductivity σ = 1/ρ, temperature coefficient of resistance R_θ = R₀(1 + αΔθ), ohmic vs non-ohmic components, and resistor color coding.

Marking a lesson complete represents finishing your study of the topic; it does not denote tested mastery.

Learning Objectives

  • State Ohm’s law, identifying physical conditions (constant temperature) required for its strict validity.
  • Calculate resistance from resistivity and dimensions: R = ρl/A, and analyze uniform stretching of wires at constant volume.
  • Explain how temperature affects resistivity in metals (positive α) and semiconductors (negative α), solving R_θ = R₀(1 + αΔθ).

Core Theory & Concepts

Electrical resistance quantifies a material's opposition to charge flow under an electric potential gradient. In metallic conductors at constant temperature, the current is strictly proportional to applied potential difference (Ohm's Law). When temperature rises, thermal lattice vibrations increase collision frequency, elevating metallic resistance while lowering semiconductor resistance.

Resistivity and Dimensions

Resistance R is proportional to length l and inversely proportional to area A: R = (ρ l) / A. Material resistivity ρ has SI unit Ω m.

R = \frac{\rho l}{A} \quad \Longleftrightarrow \quad \rho = \frac{R A}{l}

Temperature Coefficient of Resistance

Fractional change in resistance per unit temperature rise: α = (R_θ - R₀) / (R₀ Δθ). For pure metals α > 0; for semiconductors α < 0.

R_\theta = R_0 (1 + \alpha \Delta\theta)

Common Misconceptions

Misconception

Ohm’s Law V = IR is a universal law of nature that applies to all electrical components.

Physical Clarification:Ohm’s law is strictly an empirical relationship obeyed only by ohmic conductors at constant temperature. Diodes, thermistors, gas discharge tubes, and hot filament lamps violate Ohm’s law.

Syllabus Topic Outline

Competency 8.1
  • 1Ohm’s Law: physical statement and linear V-I relationship
  • 2Factors governing resistance: length, cross-sectional area, material resistivity
  • 3Formula: R = ρl / A and volume-conserving dimensional stretching
  • 4Temperature coefficient of resistance (α) and platinum resistance thermometer
  • 5Non-ohmic conductors: filament lamps, thermistors, diodes, and electrolytes
  • 64-band carbon resistor color code reading and standard tolerances