V-I Characteristics

Reading an $I$–$V$ characteristic

Potential difference, $V$, is measured across a component, while current, $I$, is measured through it. An $I$–$V$ characteristic plots potential difference on the horizontal axis and current on the vertical axis. Each point therefore describes the behaviour of the component at one operating condition.

Resistance connects the two quantities:

$R=\frac{V}{I}$

For a given potential difference, a larger current means less opposition to charge flow and therefore a lower resistance. For a non-linear component, $V/I$ can change from one point on the curve to another, so it does not have one constant resistance.

Positive and negative values show opposite polarities of potential difference and opposite directions of current. Reversing the power-supply connections produces the negative part of a characteristic.

A fixed resistor gives a straight line

For a fixed resistor under constant physical conditions, resistance remains constant. From $I=V/R$, doubling the potential difference doubles the current. Current is therefore directly proportional to potential difference.

Its $I$–$V$ characteristic is a straight line through the origin. Reversing the potential difference reverses the current, giving a matching straight-line section in the negative quadrant. A steeper straight line represents a smaller resistance because it gives more current for the same potential difference.

A filament lamp becomes more resistant

A filament lamp contains a thin metal wire. Increasing the potential difference usually increases the current, but the current heats the filament. At a higher temperature, the filament has a greater resistance, so further increases in potential difference produce progressively smaller increases in current.

The lamp's characteristic is therefore curved rather than a straight line: it is steep near the origin when the filament is relatively cool and becomes less steep as the magnitude of the potential difference and the filament temperature rise. It has a similar shape for positive and negative polarities because the lamp conducts in either direction.

Data for Illustrative $I$–$V$ characteristics of a fixed resistor and filament lamp

The two curves reveal the key distinction. The fixed resistor is an ohmic conductor with constant resistance, whereas the lamp is non-ohmic because heating changes its resistance. At any chosen point on the lamp curve, its resistance can still be found from the coordinates using $R=V/I$.

A diode conducts mainly one way

A diode behaves like a one-way electrical valve. In the forward direction, very little current flows at first; after the forward potential difference becomes sufficiently large, the current rises very rapidly. Its resistance has become much lower in this conducting region.

When the polarity is reversed, the diode has a very large resistance and the reverse current is negligible under the conditions represented at GCSE. Its characteristic is consequently very different on the two sides of the origin.

Data for Illustrative $I$–$V$ characteristic of a diode

The diode is non-ohmic: current is not directly proportional to potential difference, its resistance is not constant, and reversing the polarity changes its behaviour rather than simply reversing the current.

Comparing the three components

A fixed resistor produces a straight line through the origin because its resistance is constant. A filament lamp produces a roughly symmetrical curve because it conducts both ways but becomes hotter and more resistant as current increases. A diode produces an asymmetrical curve because it conducts readily in only its forward direction.

These shapes let you identify an unknown component from its graph and explain its behaviour in terms of whether its resistance stays constant, changes with temperature or depends strongly on current direction.

Fixed resistor

• $I\propto V$ when physical conditions are constant.
• Straight $I$–$V$ line through the origin.
• Constant resistance: $R=V/I$.
• Reversing $V$ reverses $I$ symmetrically.

Filament lamp

• Curved, roughly symmetrical characteristic.
• Increasing current heats the filament.
• Higher temperature → greater resistance → current rises less rapidly.
• Non-ohmic: resistance is not constant.

Diode

• Conducts readily only in the forward direction.
• Forward current rises rapidly once the potential difference is sufficiently large.
• Reverse resistance is very large, so reverse current is negligible.
• Asymmetrical, non-ohmic characteristic.

Graph recall

Potential difference is on the horizontal axis; current is on the vertical axis. For the same $V$, a larger $I$ means a smaller $R$. At a selected point, calculate resistance using

$R=\frac{V}{I}.$