Resistance of a wire: length and thickness sim
Slide a crocodile clip along a constantan wire, read the voltmeter and ammeter, work out R = V ÷ I, plot R against length and compare three thicknesses of wire.
Current of electricity · covers the O-Level, IGCSE, GCSE topic
What the sim shows
A 1.5 V cell drives a current through the constantan wire from the fixed end (0 cm) to the crocodile clip. The voltmeter measures the p.d. V across that length l and the ammeter measures the current I through it, so R = V ÷ I. Doubling the length doubles the resistance: R against l is a straight line through (almost) the origin, so R is proportional to l. The gradient is the resistance of one metre of wire: about 8.3 Ω/m for 0.274 mm (SWG 32) wire, 4.4 Ω/m for the thicker 0.376 mm (SWG 28) and 16.7 Ω/m for the thinner 0.193 mm (SWG 36). A thicker wire has a larger cross-sectional area A = πd²/4, so its resistance is smaller: R is proportional to 1/A. Together, R = ρl/A, where ρ (resistivity) for constantan is 4.9 × 10⁻⁷ Ω m. Your line misses the origin by a little, usually between 0.02 and 0.11 Ω: this is the contact resistance where the clip touches the wire (the voltmeter lead is on the clip). The cell has an internal resistance of 0.5 Ω, so the voltmeter reads less than 1.5 V; this does not change R = V/I. Time runs in real time only while the switch is closed (and while the wire cools after): if the switch is left on, the wire gets hot and the cell runs down, so the readings drift. Switch off between readings. Constantan is used because its resistance hardly changes as it warms (by less than 0.5% here). The warm tint on the wire is exaggerated: at these currents the wire gets hot but does not glow. The meters are taken as ideal (0.01 V and 0.001 A resolution), and the small scatter in the readings (0.3%) is simulated.
- Crocodile clip: sets the length l of wire in the circuit
- Red leads: + side · black leads: − side
- Blue glow: the length of wire carrying current
- Orange-brown: wire warmed by the current (exaggerated)
- Graph: dashed line R = (ρ/A) l through the origin
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