I-V characteristics

I-V characteristics are graphs of the current through a component (I) against the potential difference across it (V). Their shape shows how the component behaves. A resistor at constant temperature gives a straight line through the origin, so its resistance is constant. A filament lamp gives an S-shaped curve, since a hotter filament has a higher resistance. A diode only lets current through in one direction. These I-V graphs are what you plot in the GCSE required practical.

How to read an I-V graph

Potential difference goes along the x axis and current up the y axis. Positive values mean the current flows one way through the component; negative values mean the connections have been swapped, so it flows the other way. At A-level, AQA questions may put either current or potential difference on the horizontal axis, so always check which way round the axes are.

• Straight line through the origin: current is directly proportional to potential difference, so the resistance is constant. The component is linear, or ohmic.
• Curve: the resistance changes as the current changes. The component is non-linear.
• Steeper: more current for each volt, so lower resistance.
• Flatter: less current for each volt, so higher resistance.

Resistance at any point is found from R = V ÷ I, using the values at that point:

I-V characteristic of a resistor

Here x is the potential difference in volts and y is the current in amps. AQA GCSE Physics says the current through an ohmic conductor at a constant temperature is directly proportional to the potential difference across it. That gives a straight-line graph passing through (0, 0), with the same shape in both directions. At 4 V the current is 0.2 A, so R = 4 ÷ 0.2 = 20 Ω, and the same at every other point. This is Ohm's law.

Read the resistance from a graph yourself in this question from the Electricity course.

I-V characteristic of a filament lamp

Again x is the potential difference in volts and y is the current in amps. Near the origin the line is fairly steep, but it gets flatter as the potential difference rises. More current makes the thin metal filament hotter. In a hot filament the metal ions vibrate harder, the moving electrons bump into them more often, and the resistance goes up. The curve has the same shape in both directions, because the filament heats up whichever way the current flows.

Example 1: resistance of the lamp

The resistance rises from 11 Ω to 17 Ω as the lamp gets brighter and hotter. Work out V ÷ I at each point: the gradient of the curve does not give the resistance.

I-V characteristic of a diode

Here x is the potential difference in volts and y is the current in amps. AQA GCSE Physics says the current through a diode flows in one direction only, and that its resistance is very high when the p.d. is reversed. On the graph:

• Reverse direction (negative p.d.): the current is almost exactly zero. The resistance is very high.
• Forward direction, below about 0.6 V: still very little current.
• Forward direction, above about 0.6 V: the current rises very steeply, so the resistance becomes small. In this example the current is about 10 mA at 0.6 V and about 0.5 A at 0.7 V.

A light-emitting diode (LED) has the same shape of graph, with a higher turn-on voltage that depends on its colour. Diodes are used to stop current flowing the wrong way, for example to protect a circuit if a battery is put in backwards.

Thermistors and LDRs

AQA GCSE Physics also lists thermistors and light-dependent resistors (LDRs) as components whose resistance is not constant:

At a fixed temperature or light level, each gives a roughly straight I-V line. Warm the thermistor, or shine more light on the LDR, and the line gets steeper because the resistance drops.

Comparing the three I-V graphs

Check your understanding.

The circuit for measuring I-V characteristics

Required practical activity 4 in AQA GCSE Physics asks you to investigate the I-V characteristics of a filament lamp, a diode and a resistor at constant temperature. The circuit is:

• A power supply and a variable resistor, to change the potential difference.
• An ammeter in series with the component, to measure the current.
• A voltmeter in parallel across the component, to measure the potential difference.
• For a diode, a protective resistor in series, so the current cannot get too large.

1. Set the variable resistor to give a small p.d. Record V and I.
2. Change the variable resistor in steps and record each pair of readings.
3. Swap the connections to the component and repeat to get negative values.
4. Plot current on the y axis against potential difference on the x axis.

Keep the current small and switch off between readings for the resistor, so it stays at a constant temperature. You can build and test the same circuit in the Circuit Builder.

Common mistakes

• Using the gradient for resistance on a curve. Use R = V ÷ I at the point.
• Saying a steeper line means higher resistance. Steeper means more current per volt, so lower resistance.
• Forgetting "at constant temperature" for the resistor. If it heats up, its resistance changes too.
• Drawing the lamp curve getting steeper. It gets flatter as the p.d. increases.
• Giving a diode zero resistance forwards. It is low once the diode is on, but not zero.
• Putting the voltmeter in series. It goes in parallel across the component.

Practise with a short timed paper

I-V characteristics come up in GCSE Physics and in the first year of A-level Physics. The daily GCSE Physics Higher and A-level Physics: Year 1 papers are short timed papers of 8 questions, with a new one every day. For more on resistance itself, see what is a resistor.

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