Resistance and I–V Characteristics

Not every component obeys the same simple rule. For an ordinary resistor at a steady temperature, doubling the voltage doubles the current — but for a filament lamp, a diode, a thermistor or a light-dependent resistor, the relationship between current and voltage is more interesting. We investigate these relationships by measuring the I–V characteristic of a component: a graph of the current through it against the potential difference across it. The shape of this graph reveals exactly how the component's resistance behaves. This lesson, part of Topic P3 of OCR Gateway Combined Science A, describes the practical for measuring I–V characteristics, interprets the graphs for an ohmic conductor, a filament lamp and a diode, and explains the special behaviour of the thermistor and the LDR.

By the end of this lesson you should be able to describe how to investigate I–V characteristics, sketch and interpret the I–V graphs for an ohmic conductor, a filament lamp and a diode, explain how the resistance of a thermistor and an LDR changes, and state their uses.

This lesson builds AO1 understanding of thermistor and LDR behaviour, AO2 application in setting up the required practical to obtain I–V data, and strong AO3 analysis when you interpret the shapes of the I–V graphs and relate a changing gradient to a changing resistance.

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Investigating I–V Characteristics

The I–V characteristic of a component is a graph of the current $I$I through it (on the vertical axis) against the potential difference $V$V across it (on the horizontal axis). To measure it you vary the voltage across the component in steps and record the current at each step.

The circuit uses the component under test connected in series with an ammeter (to read the current through it) and a variable resistor (to change the current), with a voltmeter connected in parallel across the component (to read the p.d. across it).

Method (numbered):

1. Set up the circuit with the test component, an ammeter and a variable resistor in series, and a voltmeter in parallel across the component.
2. Adjust the variable resistor to set the potential difference to a low value, and record the voltmeter reading $V$V and the ammeter reading $I$I.
3. Increase the voltage in equal steps, recording $V$V and $I$I at each step, across a range of values.
4. To obtain readings for negative (reversed) voltages, swap over the connections to the cell (or use a supply that can reverse), so the graph can be plotted for current in both directions.
5. Plot a graph of current $I$I (vertical axis) against potential difference $V$V (horizontal axis).
6. Take readings quickly (so components do not heat up between readings) and repeat to find a mean.

Exam Tip: In the I–V practical, the ammeter goes in series with the component and the voltmeter in parallel across it, with a variable resistor to change the current. Plot $I$I on the vertical axis and $V$V on the horizontal axis.

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The Ohmic Conductor (Fixed Resistor at Constant Temperature)

An ohmic conductor — such as a fixed resistor or a length of metal wire kept at a constant temperature — gives the simplest I–V graph: a straight line through the origin. This means the current is directly proportional to the potential difference: double the voltage and you double the current. Because $R = V/I$R=V/I stays the same at every point, the resistance is constant.

This is Ohm's law: for an ohmic conductor at constant temperature, the current is directly proportional to the potential difference. The straight line works for both positive and negative voltages, so the graph passes through the origin at a constant gradient. The key condition is constant temperature — if the wire is allowed to heat up, it stops being ohmic (as the filament lamp shows).

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The Filament Lamp

A filament lamp gives a very different, S-shaped curve. At low voltages the line is steep and roughly straight, but as the voltage increases the curve bends over (flattens), showing that the current rises less and less for each extra volt. This is because the resistance increases as the lamp gets hotter.

Here is the reason: as more current flows, the metal filament heats up and glows. In a hotter metal the atoms vibrate more vigorously, so the moving electrons collide with them more often. More collisions mean more opposition to the current — a higher resistance. So as the voltage (and current) rises, the filament gets hotter, its resistance rises, and the current increases more slowly than it would for an ohmic conductor. The lamp is therefore a non-ohmic component.

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The Diode

A diode only lets current flow in one direction. Its I–V characteristic shows almost no current when the voltage is applied in the reverse direction (the diode has a very high resistance), but once the voltage in the forward direction passes a small threshold (about $0.6 \text{ V}$0.6 V for a silicon diode), the current rises steeply (the diode has a very low resistance). A diode therefore acts like a one-way valve for current, which is why it is used to make sure current flows the correct way round a circuit.

The three graphs together are worth memorising as a set:

Component	Shape of I–V graph	Resistance behaviour
Ohmic conductor (constant temperature)	Straight line through the origin	Constant ($I \propto V$I∝V)
Filament lamp	S-shaped curve that flattens	Increases as it heats up
Diode	Current only one way; steep after a small forward voltage	Very high in reverse, low in forward direction

Exam Tip: Learn the three I–V shapes: ohmic conductor = straight line through the origin; filament lamp = S-curve that bends over (resistance rises with temperature); diode = one-way (current only in the forward direction). The lamp's bending is the most-tested: it is because the filament heats up and its resistance rises.

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Thermistors

A thermistor is a component whose resistance depends on its temperature. In the type you study, the resistance falls as the temperature rises (and rises as the temperature falls). So a hot thermistor has a low resistance and a cold thermistor a high resistance.

This makes the thermistor ideal as a temperature sensor. It is used in:

• thermostats for central heating, ovens and fridges, switching the heating on or off as the temperature changes;
• fire alarms and temperature-warning circuits;
• car engine temperature sensors.