What resistance depends on
Two wires, same push. One lets more current through. Why?
- A wire of length L, area A. R = 2 Ω.
- Double the length. R doubles to 4 Ω.
- Double the area instead. R falls to 1 Ω.
- Longer raises R. Thicker lowers R.
Slide the length and the thickness. Watch R change.
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The wire with less resistance lets more current through. Length, thickness, material and temperature set the resistance.
New word
Resistivity (ρ) — a number that belongs to the material, at one temperature. Unit: ohm-metre (Ω·m).
The rule
A longer wire has more resistance. A thicker wire has less resistance. The material and temperature decide the rest.
R = ρL ÷ A
L is the length, in metres (m). A is the cross-section area. It is the face you see when the wire is cut. ρ (rho) is the material's own resistivity.
| ρ (Ω·m) | L (m) | A (m²) | R = ρL ÷ A |
|---|---|---|---|
| 1 × 10⁻⁶ | 2 | 1 × 10⁻⁶ | 2 Ω |
For that wire, R = ρL ÷ A. So R = (1 × 10⁻⁶ × 2) ÷ (1 × 10⁻⁶) = 2 Ω.
Double the length to 4 m. Then R = (1 × 10⁻⁶ × 4) ÷ (1 × 10⁻⁶) = 4 Ω.
Double the area instead, to 2 × 10⁻⁶ m². Then R = (1 × 10⁻⁶ × 2) ÷ (2 × 10⁻⁶) = 1 Ω.
Two wires can share the same length and area. Yet they can have different resistance. Their materials have different ρ. A copper wire's ρ is small, so it suits house wiring. An alloy is a metal mixed with other elements. An alloy such as nichrome has a far bigger ρ. So nichrome suits heater coils.