A 1m copper wire (d=1mm) has resistance 0.022Ω. What is R for a 3m, 0.5mm copper wire?

R ∝ L/A; new R = 0.022 × (3/1) × (1²/0.5²) = 0.022 × 3 × 4 = 0.264Ω.

Why is nichrome used in toasters instead of copper?

Nichrome has much higher resistivity → more resistance → more heat generated per meter.

How does resistance change when a wire heats up in a toaster?

R = ρ₀[1+α(T−T₀)]L/A; resistivity increases with T → R increases → slightly less current flows.

Pro 🔒~20 min

Resistance in a Wire

Explore how length, area, and material affect resistance

How it works

Resistance depends on the material's resistivity ρ (intrinsic property), wire length L, and cross-sectional area A: R = ρL/A. Longer wire = more resistance (more collisions). Thicker wire = less resistance (more paths for electrons). Resistivity varies by material (copper: 1.7×10⁻⁸ Ω·m; nichrome: 100×10⁻⁸ Ω·m) and increases with temperature for metals. This explains why heating elements use nichrome wire.

Upgrade to Pro to access this experiment

Step-by-step

Select a wire material.
Adjust length and diameter using the sliders.
The ohmmeter reads resistance in real time.
Plot R vs L (constant A) to verify the linear relationship.
Change diameter to verify R ∝ 1/A.
Change material to compare resistivities.

Key formulas

$R = \rho\frac{L}{A}$ Resistance equation
$A = \pi r^2 = \frac{\pi d^2}{4}$ Cross-sectional area
$\rho(T) = \rho_0[1 + \alpha(T - T_0)]$ Resistivity temperature dependence

Frequently asked questions

A 1m copper wire (d=1mm) has resistance 0.022Ω. What is R for a 3m, 0.5mm copper wire?: R ∝ L/A; new R = 0.022 × (3/1) × (1²/0.5²) = 0.022 × 3 × 4 = 0.264Ω.
Why is nichrome used in toasters instead of copper?: Nichrome has much higher resistivity → more resistance → more heat generated per meter.
How does resistance change when a wire heats up in a toaster?: R = ρ₀[1+α(T−T₀)]L/A; resistivity increases with T → R increases → slightly less current flows.