Resistance Recipe
Length, thickness, material, heat — cook any resistance you want
What this lesson covers
Why it matters
Power lines: fat aluminium. Heater coils: thin nichrome. Earphone wires: hair-thin copper. Same electricity — three completely different wires. Why?
The idea in plain words
The recipe behind every wire ever made. Tap the ingredients.
R = ρ·l ÷ A
A nichrome wire: l = 2 m, A = 1 mm², ρ = 1.1 Ω·mm²/m. Find R.
R = 2.2 Ω
- ohm (Ω): R — resistance of the wire
- Ω·mm²/m: ρ — resistivity — the material's own stubbornness (nichrome ≈ 65× copper)
- metre (m): l — length of the wire — longer means more resistance
- mm²: A — area of cross-section — thicker means LESS resistance
- R = ρl ÷ A = 1.1 × 2 ÷ 1
Predict first
Two copper wires are identical, except one is twice as long. The longer wire's resistance is…
R = ρl/A. Twice the length is twice the crowd of atoms to push through — double the resistance.
- double — correct
- half
- the same — resistance depends only on the material
What you do
Stretch it, fatten it, swap the metal, heat it. Build both target resistances and feel each knob of R = ρl/A.
Check yourself
Make a wire twice as thick (double A). Its resistance…
A wider pipe passes charge more easily: R ∝ 1/A.
Heat a metal wire and its resistance…
Hotter atoms vibrate harder and block the drifting electrons more often — for metals R climbs with temperature.
Best material for a heater coil?
A heater NEEDS resistance to turn current into heat; copper is too good a conductor to warm itself.
- halves — correct
- doubles
- is unchanged
- rises — correct
- falls
- is unchanged
- Nichrome — high resistivity and stands high heat — correct
- Copper — the best conductor
- Any metal works equally