Energy and Voltage in Circuits » Current-Voltage Graphs

What a current-voltage graph shows

You can now work out a resistance from one voltage and one current. But what happens to the current in a component as you turn the voltage up? Different components answer this in different ways, and a graph shows the answer at a glance.

Key terms:

• Current-voltage graph: a graph for one component with the voltage across it on the horizontal axis and the current in it on the vertical axis.
• Forward direction: the direction in which a diode lets current pass.
• Reverse direction: the opposite direction, in which a diode lets almost no current pass.

Both axes usually carry on below zero. A negative voltage simply means the supply has been connected the other way round. A negative current means the current is in the opposite direction. So the right-hand half of the graph shows the component connected one way, and the left-hand half shows it connected the other way.

The spec asks you to describe how current varies with voltage in four things: wires, resistors, metal filament lamps and diodes. Wires and resistors behave in the same way, so there are three shapes to learn.

A wire or resistor at constant temperature

Here are readings for a fixed resistor that stays at the same temperature.

Voltage in V	0	2	4	6	8
Current in A	0	0.25	0.50	0.75	1.00

Each time the voltage goes up by 2 V, the current goes up by the same amount, 0.25 A. Double the voltage and the current doubles. Remember, this pattern is called directly proportional.

Plotted on a graph, these points make a straight line through the origin (the point where both voltage and current are zero). With the supply reversed, the line carries on straight into the bottom left corner: −4 V gives −0.50 A.

A metal wire gives the same shape of graph, as long as its temperature does not change. That condition matters. If a large current makes the wire hot, its resistance changes and the line is no longer straight.

With current on the vertical axis, a steeper line means a lower resistance, because there is more current for each volt.

A metal filament lamp

A filament lamp contains a very thin coil of metal wire, the filament, which glows white hot. Here are readings for a small lamp.

Voltage in V	0	1	2	3	4	5
Current in A	0	0.20	0.30	0.36	0.40	0.43

The current still rises as the voltage rises, but by less and less each time. The first volt adds 0.20 A. The step from 3 V to 4 V adds only 0.04 A. Doubling the voltage from 2 V to 4 V does not double the current.

The graph starts at the origin, rises steeply at first, then curves and flattens. It never becomes flat and it never turns downwards. With the supply reversed, the lamp behaves in exactly the same way, so the left-hand half is the same curve turned upside down. The whole graph looks like a stretched letter S.

Why does this happen? It is a chain of four steps:

1. A larger voltage gives a larger current in the filament.
2. The larger current has a bigger heating effect, so the filament gets hotter.
3. The resistance of the metal filament increases as its temperature rises.
4. So each extra volt gives a smaller increase in current, and the graph flattens.

The lamp is really just a wire that is not at constant temperature.

A diode

A diode is a component that lets current pass in one direction only. Here are readings for a typical diode. The currents are small, so they are in mA.

Voltage in V	−2.0	−1.0	0	0.5	0.6	0.7	0.8
Current in mA	0	0	0	0	2	20	80

The three shapes side by side

Component	Shape of graph	What it tells you
Wire or fixed resistor at constant temperature	Straight line through the origin	Current is directly proportional to voltage. Resistance is constant.
Metal filament lamp	Curve through the origin that flattens, the same in both directions	Resistance increases as the filament heats up.
Diode	Flat along the axis for reverse voltages, then a steep rise above about 0.6 V forwards	Current in one direction only. Very high resistance in the reverse direction.

How these readings are collected is covered in the lesson Investigating Current and Voltage.

Exam-style question

A student records the current in component X for different voltages across it.

Voltage in V	0	1.5	3.0	4.5	6.0
Current in A	0	0.03	0.06	0.09	0.12

(a) Describe the shape of the current-voltage graph for component X. [2 marks]

(b) Calculate the resistance of component X when the voltage is 3.0 V. [2 marks]

(c) Component X is replaced with a metal filament lamp. Describe how the shape of the graph for the lamp is different, and explain why. [4 marks]

(d) The lamp is replaced with a diode connected in the forward direction, so there is a current. State what happens to the current when the connections to the supply are reversed. [1 mark]