Ohm’s Law and Temperature
A battery is connected to a light bulb. A current flows. It experiences resistance when it goes through the light bulb. The potential difference V and current I are related by Ohm's law: R = V / I.
R is the resistance. For a piece of metal at room temperature, resistance is roughly constant. This means that if V is doubled, then I is also doubled. If V is increased by 3 times, then I increases by 3 times also. If we plot a graph of V against I, we get a straight line.
If we change to a metal with a higher resistance, R is larger. From Ohm's law, R = V / I, this means more potential difference to keep the same current. If R is a constant, a graph of V against I is still a straight line. But this line is steeper.
It often happens that as current is increased, the metal gets hot. A common example is the light bulb. The filament in the light bulb is made of tungsten. It gets so hot that it gives out light. This heat energy comes from work done by charge as it goes against the resistance of the tungsten filament in the light bulb.
We can measure the potential difference V across the light bulb and the current through it. If we plot a graph, this graph would not be a straight line. It would be a curve that curves upwards.
This means that for higher current, the potential difference is higher than expected for a straight line. This in turn means that resistance is higher. This means that Ohm's law is not obeyed by the light bulb.