Resistance, Collisions and Temperature
Look inside a 3D copper sample: ion cores vibrating in a staggered lattice while a single electron zig-zags between them, with its collisions counted live. The vibration amplitude follows the square root of the absolute temperature, so R climbs in a straight line — starting from R₀, never from the origin.
Como usar esta simulação
- Drag the temperature slider and watch the collision counter respond
- Press Double 100 → 200 °C to test whether doubling the temperature doubles the resistance
- Press Extrapolate back to follow the straight line down towards the axis
- Press Hide the casing to see the lattice and the electron path unobstructed
O que observar
- Collisions per second climb steadily as the lattice vibration amplitude grows
- Doubling the Celsius temperature does not double the resistance, because the line misses the origin
- The R–t graph is a straight line cutting the axis at R₀, the resistance at 0 °C
- Extrapolating to zero resistance points far below 0 °C rather than to it
- The ion cores never leave their sites — only the size of their vibration changes
A física por trás
Resistance comes from electrons colliding with vibrating lattice ions. Raising the temperature increases the vibration amplitude, so each core sweeps a larger area, the electron's mean free path shortens and collisions become more frequent. Over the ordinary range this gives the linear law R = R₀(1 + αt), where R₀ is the resistance at 0 °C and α is the temperature coefficient. The line is straight but does not pass through the origin: extrapolating back to zero resistance reaches a temperature well below 0 °C, which is why R₀ and not zero is the intercept.