Current-potential difference graphs

1. A current-potential difference graph shows how the current through a component changes as the potential difference across it changes.
2. The potential difference is the independent variable, so it is plotted on the horizontal axis, in volts, $V$.
3. The current is the dependent variable, so it is plotted on the vertical axis, in amperes, $A$.
4. Positive values show the current in one direction, and negative values show the current flowing the opposite way after the supply connections are reversed.
5. The resistance at any point on the graph is found by reading off $V$ and $I$ at that point and calculating $R=\frac{V}{I}$.
   1. A steeper line means more current for each volt, so it shows a smaller resistance.
   2. A shallower line means less current for each volt, so it shows a larger resistance.

Linear components

1. The graph of a linear component is a straight line through the origin.
2. Equal increases in potential difference produce equal increases in current, so the current is directly proportional to the potential difference.
3. Because $\frac{V}{I}$ is the same at every point on the line, a linear component has a constant resistance.
4. A fixed resistor and a metal wire at constant temperature are linear components.
5. The line has the same shape for negative values, because these components behave in the same way whichever direction the current flows.
6. Two linear components can be compared by the steepness of their lines, with the steeper line belonging to the component with the smaller resistance.

Non-linear components

1. The graph of a non-linear component is curved.
2. Equal increases in potential difference produce unequal changes in current, so the current is not directly proportional to the potential difference.
3. Because $\frac{V}{I}$ is different at different points on the curve, a non-linear component has a resistance that changes.
4. The direction in which the curve bends shows how the resistance changes.
   1. A curve that becomes less steep as the potential difference increases shows a resistance that is increasing.
   2. A curve that becomes steeper as the potential difference increases shows a resistance that is decreasing.
5. A filament lamp, a diode and a thermistor that warms up as the current increases are all non-linear components.

Deciding from data

1. To decide from a table of results, calculate $\frac{I}{V}$ or $\frac{V}{I}$ for each row.
   1. If the ratio is the same for every row, the component is linear.
   2. If the ratio changes steadily from row to row, the component is non-linear.
2. To decide from a graph, lay a ruler along the plotted points and check whether they lie on a straight line that passes through the origin.
3. A single point that lies well away from an otherwise smooth pattern is an anomaly and should be checked or repeated, not used to change the line.