Practical: Investigating I-V Characteristics

Measuring the resistance of a component

Resistance describes how strongly a component opposes current. To find it, measure the current $I$ through the component and the potential difference $V$ across it, then use

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

where resistance is measured in ohms ($\Omega$), potential difference in volts (V) and current in amperes (A).

The ammeter must be in series so that the same current that passes through the component also passes through the meter. The voltmeter must be in parallel across the component because it compares the energy transferred per unit charge on the two sides of that component. A variable resistor in series allows the current, and therefore the potential difference across the test component, to be changed safely.

For a component whose resistance changes, $V/I$ gives its resistance at that particular operating point. A fixed resistor at constant temperature has an approximately constant value of $V/I$, but a filament lamp and a diode do not.

The purpose of the I–V investigation

An I–V characteristic shows how the current through a component responds when the potential difference across it changes. The independent variable is the potential difference and the dependent variable is the current. The component being tested is changed between a fixed resistor, a filament lamp and a diode.

The basic apparatus is a low-voltage supply or battery, an ammeter, a voltmeter, a variable resistor, connecting leads and the test component. A milliammeter may be used for the smaller diode currents. A diode also needs a protective resistor in series to prevent an excessive current from damaging it.

Taking the measurements

1. Construct the circuit from its circuit diagram. Check that the ammeter and variable resistor are in series and that the voltmeter is across the test component.
2. Set the variable resistor to limit the current before switching on.
3. Record the potential difference across the component and the current through it.
4. Adjust the variable resistor to obtain a suitable range of potential differences, recording a pair of readings each time.
5. Switch off between readings where practical. This reduces unwanted heating, which is especially important when testing whether a fixed resistor is ohmic at constant temperature.
6. Repeat readings where appropriate, identify anomalous results and calculate means.
7. Switch off before reversing the supply connections. Repeat the measurements to obtain negative potential differences and currents. For a diode, this tests both its forward and reverse directions.
8. Replace the component and repeat the procedure for the filament lamp and diode, using the protective resistor and a suitably sensitive current meter for the diode.

Use a low potential difference initially. Components and wires can become hot, so disconnect the supply when readings are not being taken and allow hot components to cool before handling them.

Plotting the results

Plot potential difference in volts on the horizontal axis and current in amperes, or milliamperes where appropriate, on the vertical axis. Use a sensible scale, plot each point accurately and draw a smooth curve or line of best fit rather than joining points dot to dot.

For a fixed resistor at constant temperature, the graph is a straight line through the origin. Doubling the potential difference doubles the current, so $V/I$ and therefore the resistance remain constant. It is an ohmic conductor.

The filament lamp produces a curve that becomes less steep as the magnitude of the potential difference increases. A larger current heats the filament; its resistance rises, so each further increase in potential difference produces a proportionally smaller increase in current. The curve has a similar shape for positive and negative values because the lamp conducts in either direction.

A diode conducts mainly in one direction. In reverse bias it has a very high resistance, so the current is extremely small. In forward bias there is initially little current, followed by a rapid increase once the potential difference is large enough for appreciable conduction. Its I–V characteristic is therefore strongly non-linear and is not symmetrical about the origin.

Connecting the circuit, calculation and graph

The circuit provides two readings at every setting: $I$ describes the flow through the component and $V$ describes the energy transfer across it. Their ratio gives resistance, while the full collection of pairs reveals whether that resistance stays constant or changes. This is why one reading can measure resistance at one operating point, but several readings and an I–V graph are needed to describe a component's electrical behaviour.

Circuit recall

• Ammeter: series with the component.
• Voltmeter: parallel across the component.
• Variable resistor: changes and limits current.
• Resistance: $R=V/I$.
• Use a protective series resistor with a diode.

Practical sequence

Construct and check the circuit → begin with a low current → record paired $V$ and $I$ readings → vary the setting → switch off before reversing the supply → repeat for the resistor, lamp and diode → plot $I$ against $V$.

Keep a fixed resistor at approximately constant temperature by using low currents and switching off between readings. Disconnect the supply before altering the circuit.

Characteristic shapes

• Fixed resistor at constant temperature: straight line through the origin; $I\propto V$ and resistance is constant.
• Filament lamp: curved in both directions; heating raises resistance, so the curve becomes less steep at larger $|V|$.
• Diode: appreciable current mainly in the forward direction; very high resistance and almost no current in reverse bias.

For a non-linear component, $V/I$ can differ from one point on the curve to another.