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 (Electricity) of OCR Gateway Science A, describes the required 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 the required practical for investigating 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.

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Required Practical: 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 need to 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 the readings for negative (reversed) voltages, swap over the connections to the cell (or use a power supply that can reverse) and repeat, 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. To get reliable readings, take the measurements quickly (so components do not heat up between readings) and repeat to find a mean.

A few practical precautions improve the results. Take each pair of readings quickly and switch off between readings, so that a component such as the filament lamp does not sit and heat up (which would change its resistance and distort the graph). Use a suitable range of voltages — small enough not to damage the component but large enough to show the shape clearly — and take readings at regular intervals so the curve is well defined. Repeating each reading and finding a mean reduces the effect of random error. For the lamp and diode, where the line is curved, plenty of closely spaced points are needed to reveal the shape.

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 is a straight line passing 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: