3.4 Resistivity and Resistance

What is Resistance?

Resistance (R) measures how much a material opposes current flow, measured in ohms (Ω). It depends on the object's geometry and material. For a wire, R = ρL/A, where L is length, A is cross-sectional area, and ρ is resistivity. Longer, thinner wires have more resistance.

Resistivity: A Material Property

Resistivity (ρ) is an intrinsic property of a material, independent of its shape, measured in ohm·meters (Ω·m). Conductors like copper have low resistivity; insulators have high resistivity. Unlike resistance, resistivity doesn't change with length or area, but it does increase with temperature for most metals.

How Geometry Affects Resistance

Since R = ρL/A, increasing length increases resistance (more collisions for electrons), while increasing cross-sectional area decreases resistance (more paths for current). This explains why thick wires carry current more efficiently than thin wires of the same material and length.

Key terms

Resistance (R)

A measure of how much an object opposes current flow, in ohms (Ω); depends on material and geometry.

Resistivity (ρ)

An intrinsic material property describing how strongly it resists current, measured in Ω·m; independent of shape.

Resistance formula

R = ρL/A, where L is length and A is cross-sectional area.

Effect of length on resistance

Resistance increases proportionally with length (longer wire = more resistance).

Effect of area on resistance

Resistance decreases as cross-sectional area increases (more room for current to flow).

Try an AP-style question

A wire's length doubles (same material and thickness). What happens to its resistance?

1. It quadruples
2. It doubles
3. It halves
4. It stays the same