# Gradient and resistance - a warning

## Resistance equals slope only works for straight lines

If you plot voltage against current for a resistor then the gradient of the line is numerically equal to the resistance. But beware! This is only because the line is straight.

## Resistance is not about rates of change

For a bulb the line is curved. Even though a steepening curve corresponds to an increasing resistance, the two are only peripherally related and the gradient at a point is *not* equal to the resistance at that point.

This is because the resistance is the voltage divided by the current at a particular point. It's not the *change* in voltage divided by the *change* in current at that point, which is what the gradient represents.

## Intersection rather than equal gradients

If you have two voltage-current curves then the resistances are equal where the lines intersect. If you think about it, if both the voltage and the current are the same for the two components at that point then the resistance must also be the same.

The voltage where the two gradients are the same doesn't have any physical meaning. It's just a feature of the graph.