Resistor

What to observe

1. Watch a single electron with Follow one electron on. It does not sail down the wire. It rattles, gets grabbed by the field for a moment, slams into the lattice, forgets which way it was going, and starts over. The current is not the speed of that rattling, it is the tinynet crawl the rattling has on top of it.
2. Turn thermal motion off. Now the drift is all that is left and it is obvious. Turn it back on and it vanishes into the noise, which is honest: the thermal speed is around a million times the drift speed. Both numbers are in the readout, and the ratio is the reason a wire carrying amps still looks like nothing is happening.
3. The graph of average velocity settles onto a flat line. That is the whole of Ohm's law: the field accelerates, so without collisions the speed would grow forever, but a collision every τ seconds keeps resetting it. The average lands at aτ, proportional to the field, and current proportional to voltage is nothing but that.
4. Make the sample twice as long. The same voltage is now spread over twice the distance, so the field is halved, so the drift is halved, soR doubles. Now make it twice as fat instead: same field, same drift, but twice as many lanes carrying it, so R halves. That is the whole content of R = ρL/A, and neither half of it needed an experiment.
5. Raise the temperature. The lattice shakes harder, an electron gets less far before hitting something, τ falls and resistance rises. Carbon does the opposite, because heat there frees more carriers than it scatters, and that sign difference is why carbon and metal resistors age and drift in opposite directions.
6. Every collision hands the field's energy to the lattice, which is whereP = VI physically goes. Switch on let it heat itself up with tungsten and turn the voltage to full. The metal glows, its resistance climbs as it does, and on the I–V plot the line bends over: a light bulb is not an ohmic device, it just contains one when it is cold.
7. Compare copper with nichrome at the same size. Copper's resistivity is about sixty times lower, so at a few volts it draws an absurd current and cooks itself. That is why one of them is sold as wire and the other as a heating element: same physics, different τ.