Component Resistance and Current–Voltage Characteristics

What an I–V characteristic tells us

Two components connected to the same potential difference need not carry the same current: their resistances may differ. An I–V characteristic shows this behaviour by plotting current, $I$, through a component against potential difference, $V$, across it. Current is measured in amperes (A) and potential difference in volts (V).

For any non-zero current reading, the component’s resistance can be calculated using:

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

Resistance is measured in ohms ($\Omega$). Comparing this ratio at different points tells us whether the resistance stays constant or changes as the current changes.

Fixed resistors: a proportional relationship

A fixed resistor has approximately constant resistance, provided its temperature remains constant. Doubling the potential difference therefore doubles the current. Its I–V graph is a straight line through the origin: current is directly proportional to potential difference. This is a linear circuit element and is described as obeying Ohm’s law.

On these axes, a steeper straight line means more current flows for the same potential difference, so the resistance is lower. A shallower line means a higher resistance. Reversing the supply reverses the current, giving a straight-line continuation into the negative part of the graph.

Lamp filaments and heating elements: resistance rises as they heat

A filament lamp behaves differently. Current transfers energy to the thin metal filament, increasing its temperature until it glows. As the metal gets hotter, its atoms vibrate more strongly and impede the movement of electrons more. Its resistance increases.

Consequently, increasing the potential difference still increases the current, but not proportionally. On an I–V graph, the curve becomes less steep as the magnitude of the potential difference increases. The lamp is a non-linear circuit element. Reversing the supply reverses the current but produces the same heating behaviour, so the graph has corresponding positive and negative branches.

Metal heating elements also increase in resistance as current heats them. Their purpose is to transfer energy by heating, whereas a lamp filament becomes hot enough to emit visible light.

Diodes: direction matters

A diode allows current to flow readily in one direction, called the forward direction. Even in this direction, little current flows at very small potential differences; after the forward potential difference becomes sufficient, the current rises steeply. The graph is therefore non-linear.

With the supply reversed, the diode has a very high resistance and the current is approximately zero over the safe operating range. Unlike a resistor or lamp, its graph is not symmetrical about the origin. This one-way behaviour allows a diode to control the direction of current. An LED is a light-emitting diode: it emits light when a suitable forward current flows.

To interpret a characteristic, first check the axes, then look for a straight line through the origin, curvature and any difference between the two directions. Link these observations to constant resistance, heating or one-way conduction rather than simply naming the shape.

Measuring a component’s I–V characteristic

Use a low-voltage d.c. supply, connecting leads, an ammeter, a voltmeter and the component being tested. A variable resistor in series provides a way to vary the current and the potential difference across the test component. Alternatively, a variable d.c. power supply can vary the potential difference directly.

The ammeter goes in series so it measures the current through the component. The voltmeter goes in parallel across the component so it measures the potential difference between its two terminals. Use that voltmeter reading, rather than the supply setting: other parts of the circuit may also have a potential difference across them.

1. Build the circuit with the supply switched off. Start with a low supply setting and a high resistance on the variable resistor. Have the connections checked before switching on.
2. Switch on and record a pair of readings: potential difference across the test component and current through it.
3. Change the setting in small steps. At each setting, allow the readings to settle and record another pair. Collect enough readings across the safe operating range to reveal the shape, taking more where the current changes rapidly.
4. Switch off before reversing the supply connections. Repeat within the component’s safe limits, recording reversed potential difference and current as negative values.
5. Plot $$ vertically against horizontally, label both axes with units, and draw a suitable best-fit line or smooth curve. Repeat readings where necessary to check consistency.

Use the same arrangement for a fixed resistor, filament lamp or diode, replacing only the test component. For a fixed resistor, avoid appreciable heating so that its temperature stays approximately constant. For a lamp, let the readings settle at each setting so that the filament’s temperature is reasonably steady.

Use a current-limiting resistor or a suitably current-limited supply when testing a diode or LED. Do not exceed component ratings, including the permitted reverse potential difference. Lamps and resistors can become hot: switch off before changing components and allow them to cool before touching them. The investigation is complete when the readings cover the intended safe range and clearly establish the characteristic—not when a component overheats.

LDRs and thermistors: controlling the surroundings

An LDR responds to light. Its resistance decreases as the light intensity reaching it increases. At the same potential difference, it therefore carries more current in brighter light. This makes it useful in light-sensitive circuits, such as automatic outdoor lighting.

A thermistor responds to temperature. For the type studied here, its resistance decreases as temperature increases. At the same potential difference, a warmer thermistor carries more current. This makes it useful in temperature-sensing circuits, such as electronic thermostats.

To investigate their I–V characteristics, put the LDR or thermistor in the test-component position in the same measuring circuit. For an LDR, keep the illumination fixed while varying the potential difference and recording paired $V$ and $I$ readings. Repeat at a different fixed illumination. A separate lamp can provide the light; keep other lighting conditions controlled and avoid heating the LDR.

For a thermistor, keep its temperature steady while collecting each set of paired readings. Repeat at a different temperature, using controlled external heating and a thermometer to monitor temperature. Keep the heater close but not touching the thermistor, allow time for the temperature and readings to settle, and take care around hot equipment. Use small measuring currents to minimise heating by the current itself.

Plot and compare the I–V graphs, and calculate $V/I$ at selected points. Brighter conditions should give a lower LDR resistance; warmer conditions should give a lower thermistor resistance. Whether an individual characteristic is linear must be judged from the graph under the stated conditions. An environmental change in resistance is not, by itself, proof that current and potential difference have a non-linear relationship at a fixed environment.

Recognise the characteristic

• Fixed resistor: straight line through the origin; constant resistance at constant temperature; $I \propto V$.