How to play Wire Stretcher
- Choose a test and read the wire and the change on the card.
- Use R = ρ·L ÷ A with A in m², or think in proportions: R ∝ L and R ∝ 1 ÷ d².
- Type your prediction and press Start. The wire unrolls, grows, thickens, or stretches, and the ohmmeter follows.
- Compare the ohmmeter and the graph with your orange prediction.
Length and thickness set resistance
A wire resists the current along it, and how much depends on three things: its length, its thickness, and the metal. A longer wire is a longer path, so its resistance grows in proportion to the length. A thicker wire gives the current more room side by side, so its resistance falls in proportion to the cross-section. The metal enters through its resistivity ρ: copper is very low, which is why it is used for wiring, while nichrome is about 65 times higher, which is why it is used in heaters. Together, R = ρ·L ÷ A. For a round wire the cross-section is A = π·d² ÷ 4, so doubling the diameter makes A four times larger and R a quarter. Stretching a wire to twice its length at the same volume does two things at once: the length doubles and the cross-section halves, so R grows four times.
A focused learning model
The wire is a uniform round conductor at room temperature with a fixed resistivity: copper 1.68 × 10⁻⁸ Ω·m, nichrome 1.10 × 10⁻⁶ Ω·m. The wires of tests 2 to 4 are nichrome, with the lengths and cross-sections that give their starting resistances. Each change is made steadily over 2 s and held for 1 s; stretching keeps the volume, so the cross-section falls as the length grows. The ohmmeter is ideal and the clamps add no resistance. Answers within 2% are right.