Resistance and I–V Characteristics

For an ohmic conductor at constant temperature, current is directly proportional to potential difference. Doubling the potential difference doubles the current; tripling it triples the current. The ratio $V/I$ therefore stays the same, so the resistance is constant.

A suitable fixed resistor behaves this way as long as its temperature remains constant. A variable resistor lets you deliberately adjust the resistance; once its setting is fixed, it can also behave as an ohmic conductor at constant temperature.

On a graph with potential difference on the horizontal axis and current on the vertical axis, an ohmic conductor produces a straight line through the origin. It is a linear component. Reversing the potential difference reverses the current, giving the same straight-line relationship in the negative region.

For this choice of axes, the gradient is $I/V = 1/R$. A steeper line means more current for the same potential difference, so it represents a lower resistance.

A filament lamp’s resistance rises as it heats up

A filament lamp contains a thin metal wire. Current heats the filament until it emits light. As the current increases, the filament becomes hotter and its resistance increases.

At a higher temperature, the atoms in the metal vibrate more strongly. Electrons moving through the filament encounter more collisions, making it harder for charge to flow. Increasing the potential difference still increases the current, but the current increases less rapidly as the filament gets hotter.

The lamp’s I–V graph therefore curves and becomes less steep at larger potential differences. It is non-linear: current and potential difference are not directly proportional. Reversing the potential difference reverses the current, but the filament heats in either direction, so the curve has a matching shape in the negative region.

A diode behaves differently in the two directions

A diode allows current to flow in one direction only. Connected in the conducting direction, it is forward biased. At small forward potential differences, very little current flows; as the potential difference increases sufficiently, the current rises sharply.

Connected in the opposite direction, it is reverse biased. Its resistance is very high, so the current is effectively zero over the range used in this investigation. This one-way behaviour is useful when a circuit needs to prevent current flowing in the wrong direction.

A diode’s I–V graph is non-linear and, unlike the lamp’s graph, is not symmetrical about the origin. The forward side rises sharply, whereas the reverse side lies very close to the horizontal axis.

Other components, including thermistors and light-dependent resistors (LDRs), also have resistance that is not always constant. Their responses to temperature and light are considered separately.

Build a circuit that measures the component itself

To investigate resistance, you need a low-voltage d.c. supply, connecting leads, an ammeter, a voltmeter, a variable resistor and the component being tested.

The ammeter goes in series with the component so it measures the current passing through it. The voltmeter goes in parallel across the component so it measures the potential difference between the component’s two ends. The variable resistor is in series and allows you to change the current and the potential difference across the test component. An adjustable d.c. supply can also be used to vary the potential difference.

When drawing the circuit, use standard symbols: a rectangle for a resistor, a rectangle with a diagonal arrow for a variable resistor, and circles containing A and V for the meters. Keep the voltmeter connected across the test component when replacing the resistor with a lamp or diode.

Required practical: collect the I–V characteristics

The investigation compares a resistor at constant temperature, a filament lamp and a diode.

1. Construct the measuring circuit with the fixed resistor as the test component. Begin with a low potential difference across it.
2. Record the voltmeter and ammeter readings together. These form one pair of values for the graph.
3. Adjust the variable resistor or supply to change the potential difference. Record several pairs of readings across a suitable range, staying within the component’s rating.
4. Keep the fixed resistor’s temperature as constant as possible. Use small currents and disconnect the supply between readings to reduce unwanted heating.
5. Switch off before reversing the supply connections. Collect readings with the potential difference and current reversed, recording these as negative values.
6. Replace the fixed resistor with the filament lamp and repeat. Heating of the filament is part of the behaviour being investigated, so the lamp’s resistance is expected to change.
7. Repeat with the diode, adding a protective resistor in series to limit the current. Keep the voltmeter across the diode alone. Use a suitable milliammeter range for small currents and take closely spaced readings where the forward current begins to rise sharply. Investigate both directions.

Components and wires can become hot. Disconnect the supply when not taking readings, switch off before changing connections, and allow hot components to cool before handling them. Excessive potential difference or current can damage components.

Use the results to identify the behaviour

Plot current against potential difference for each component, with labelled axes and units. Draw a suitable best-fit line or smooth curve rather than joining every point with straight segments.

A straight line through the origin supports constant resistance and ohmic behaviour under the conditions tested. A lamp curve that becomes less steep shows that current is increasing less rapidly as the filament heats. A diode curve with negligible reverse current and a sharp forward rise shows its one-way conducting behaviour.

You can also calculate $V/I$ at different non-zero points. Equal ratios indicate constant resistance; changing ratios indicate changing resistance. This connects the graph’s shape to the measurements rather than relying only on recognising a familiar outline.

• Ohmic conductor: at constant temperature, $I \propto V$ and resistance stays constant. I–V graph: straight line through the origin.
• Filament lamp: greater current heats the filament, increasing resistance. I–V graph: curve that becomes less steep; matching behaviour in both directions.
• Diode: conducts in one direction; very high reverse resistance. I–V graph: negligible reverse current and a sharp forward rise.

Measuring resistance

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

$V$: volts; $I$: amperes; $R$: ohms.

Ammeter in series; voltmeter in parallel across the test component. Vary the potential difference using a variable resistor or adjustable supply.

Required practical and graphs

• Collect paired current and potential difference readings for a resistor, lamp and diode, including reversed polarity.
• Keep the fixed resistor at constant temperature; use a protective series resistor with the diode.
• Plot current vertically against potential difference horizontally.
• Straight line through the origin: linear, constant resistance. Curved relationship: non-linear, changing resistance.
• For an ohmic conductor on these axes, gradient $= 1/R$.