Summary
Highlights
Resistance is proportional to the length of a wire. A longer wire offers higher resistance because electrons travel through more positive ions.
Resistance is inversely proportional to the cross-sectional area of a wire. A larger cross-sectional area provides more paths for electrons, leading to lower resistance.
Different materials have different electrical resistance properties. Resistivity (symbolized by 'ρ') is introduced as a measure of a material's intrinsic electrical resistance, independent of its dimensions. Resistance (R) is calculated as ρ * (Length / Area).
Using dimensional analysis, the units for resistivity are derived. Rewriting the formula R = ρ * (L/A) to solve for ρ gives ρ = R * (A/L). Since resistance is in ohms (Ω), area in meters squared (m²), and length in meters (m), the unit for resistivity is ohm-meters (Ωm).
Examples of resistivity for copper (1.7 x 10^-8 Ωm) and steel (6.9 x 10^-7 Ωm) are provided, showing that steel has much higher resistivity and thus higher resistance for the same dimensions.
Resistance is a geometric property, dependent on an object's size and material. Resistivity is an intrinsic property of a material, independent of its geometry. Doubling the length or halving the cross-sectional area changes resistance but not resistivity.