A current-voltage graph shows what a component's resistance is doing

1. The graph plots the current through a component on the vertical axis against the p.d. across it on the horizontal axis.
2. Negative values are usually shown as well, because the supply is reversed part way through to test the component both ways round.
3. The resistance at any point on the graph is $R=\frac{V}{I}$, using the coordinates of that point.
4. For a straight line through the origin the gradient is $\frac{1}{R}$, so a steeper line means a smaller resistance.
5. A curve that flattens as you move along it means the resistance is rising, and one that gets steeper means the resistance is falling.

A resistor of constant resistance gives a straight line through the origin

1. The graph is a straight line passing through the origin, continuing into the third quadrant when the supply is reversed.
2. Current is directly proportional to p.d., so doubling the p.d. doubles the current.
3. The ratio $\frac{V}{I}$ is the same at every point on the line, which is exactly what "constant resistance" means.
4. The line is equally straight in both directions, because the resistor behaves identically whichever way round the p.d. is applied.
5. This holds only while the temperature stays constant, which in practice means keeping the current small enough that the resistor does not warm up.

A filament lamp curves over because the filament gets hot

1. At low p.d. the graph starts out as a straight line through the origin, because the filament is still nearly cold.
2. As the p.d. rises the line bends over towards the p.d. axis, so equal increases in p.d. produce smaller and smaller increases in current.
3. Flattening means the resistance is increasing, because $\frac{V}{I}$ is getting larger as you move out along the curve.
4. The cause is temperature, and the chain runs in one direction.
   1. A larger current heats the metal filament.
   2. Its positive ions vibrate more as the temperature rises.
   3. The drifting electrons therefore collide with them more often.
   4. The electrons are held back more, so the resistance rises.
5. Reversing the p.d. gives an identical curve in the third quadrant, because a lamp works the same way round either way, so the finished sketch is an S-shape through the origin.

A diode conducts one way and blocks the other

1. In the forward direction almost no current flows until the p.d. reaches about $0.6V$, and then the current rises very steeply.
2. That steep rise means the forward resistance is very low once the diode has switched on.
3. In the reverse direction the current stays effectively zero however large the p.d., so the reverse resistance is extremely high.
4. The finished sketch is therefore flat along the negative p.d. axis, flat along the first stretch of the positive axis, and then sharply rising.
5. This one-way behaviour is what lets a diode turn a.c. into d.c., and it is why an LED only lights when it is connected the right way round.