I-V Characteristics: Ohmic Conductors and Ohm's Law Revision Notes | A Level AQA Physics

1. Why I-V Graphs Are the Fingerprint of a Component

Every electrical component has a story, and its I-V characteristic graph tells that story at a glance. Plot potential difference on one axis and current on the other, and the shape of the curve reveals exactly how the component behaves — whether its resistance stays fixed, rises with temperature, or switches on only above a threshold voltage.

This lesson covers three components that AQA expects you to know in detail: the ohmic conductor (such as a resistor at constant temperature), the filament lamp, and the semiconductor diode. Each produces a distinctly different graph, and understanding why the shapes differ is what separates a grade 7 answer from a grade 9 one.

2. Ohm's Law and the Ohmic Conductor

Start with the simplest case. Imagine connecting a resistor to a variable power supply and recording the current at each voltage setting. You would find that doubling the voltage doubles the current, tripling the voltage triples the current — a perfect straight-line relationship through the origin.

The phrase 'provided physical conditions remain constant' is doing a lot of work in that definition. Ohm's law is not a universal law of nature — it is a special case that applies only when temperature (and other physical conditions) do not change. A metal wire at a fixed temperature obeys it; the same wire glowing red-hot does not.

On an I-V graph, an ohmic conductor produces a straight line passing through the origin. The gradient of that line equals $\frac{I}{V}$, which is the reciprocal of resistance. A steeper line means lower resistance; a shallower line means higher resistance.

One subtlety worth flagging: $R = V/I$ is the definition of resistance and applies to every component at every operating point. Ohm's law is the additional claim that $R$ stays constant as $V$ changes. These are two different statements, and examiners test whether you can distinguish them.

3. The Filament Lamp: Resistance That Rises with Temperature

Now consider what happens when the component heats up significantly as current flows through it. A filament lamp is the classic example: the tungsten filament reaches temperatures of around 2500 °C when operating normally, and at that temperature its resistance is far higher than when it is cold.

On an I-V graph, the filament lamp produces a curve that starts steep (low resistance when cold) and progressively flattens as voltage increases (higher resistance as the filament heats up). The curve is symmetric about the origin — reversing the voltage direction gives the same shaped curve on the negative side, because the lamp behaves the same way regardless of current direction.

The physical reason for this behaviour: in a metal, increasing temperature causes the positive ions in the lattice to vibrate with greater amplitude. Conduction electrons collide with these ions more frequently, making it harder for them to flow — resistance increases. This is why the I-V curve bends away from the straight-line prediction of Ohm's law.

Notice that for the filament lamp, the gradient of the I-V curve decreases as voltage increases. Since gradient here represents $\frac{\Delta I}{\Delta V} = \frac{1}{R}$, a decreasing gradient means increasing resistance. You can read off the resistance at any point by calculating $R = V/I$ using the coordinates of that point — not the gradient of the tangent.

4. The Semiconductor Diode: A One-Way Gate

The semiconductor diode has the most dramatic I-V characteristic of the three. Unlike the ohmic conductor or the filament lamp, it behaves completely differently depending on which way round it is connected — it is not symmetric about the origin.

In the forward bias direction (positive voltage applied across the diode in the correct orientation), almost no current flows until the voltage reaches approximately 0.6–0.7 V for a silicon diode. Above this threshold, current rises very steeply — the resistance drops dramatically and the diode conducts freely. In the reverse bias direction, the diode blocks current almost entirely; resistance is extremely high and only a negligible leakage current flows.

The I-V graph therefore shows: a near-flat line along the voltage axis for negative voltages (reverse bias, very high resistance), a near-flat line along the voltage axis for small positive voltages below the threshold, and then a near-vertical rise in current once the forward threshold is exceeded. This asymmetric shape is the defining feature of a diode and is fundamentally different from both the straight line of an ohmic conductor and the symmetric curve of a filament lamp.

5. Reading I-V Graphs: Axes, Gradients, and Resistance

AQA explicitly states that exam questions may place either $I$ or $V$ on the horizontal axis. This catches many students out. The shape of the characteristic is the same physical reality — only the orientation of the graph changes.

When $V$ is on the horizontal axis (the more common convention), the gradient at any point equals $\frac{\Delta I}{\Delta V} = \frac{1}{R}$. A steeper gradient means lower resistance. When $I$ is on the horizontal axis, the gradient becomes $\frac{\Delta V}{\Delta I} = R$ directly. A steeper gradient now means higher resistance. Always check the axis labels before interpreting a gradient.

To find the resistance at a specific operating point on any I-V graph, read off the $V$ and $I$ coordinates of that point and calculate $R = V/I$. Do not use the gradient of the curve at that point — that gives you how resistance is changing, not what resistance is at that instant.

6. Worked Calculation: Finding Resistance from an I-V Graph

Theory is clearest when anchored to numbers. The following worked example walks through how to extract resistance from a characteristic graph — a skill that appears regularly in AQA data-response questions.

Worked example: Calculating Resistance at an Operating Point

A filament lamp I-V graph shows that when the potential difference across the lamp is 4.0 V, the current through it is 0.80 A. Calculate the resistance of the lamp at this operating point. [2 marks]

1. $R = \frac{V}{I}$ — [M1] Selecting the correct equation. This is the definition of resistance and applies at any operating point, whether the component is ohmic or not.
2. $R = \frac{4.0 \text{ V}}{0.80 \text{ A}}$ — Read $V = 4.0$ V and $I = 0.80$ A directly from the graph coordinates. Carry units through the substitution.
3. $R = \frac{4.0}{0.80} = 5.0 \text{ Ω}$ — [A1] $4.0 \div 0.80 = 5.0$. Check: $5.0 \times 0.80 = 4.0$ V — consistent with the original values.
4. $R = 5.0 \text{ Ω at } V = 4.0 \text{ V}$ — Always specify the operating point when quoting resistance for a non-ohmic component, because resistance varies across the curve. For an ohmic conductor this qualification is unnecessary since R is constant.

Answer: $R = 5.0$ Ω at an operating potential difference of 4.0 V

7. Required Practical: Investigating I-V Characteristics

AQA's required practical for this topic asks you to obtain I-V characteristics for a range of components. The circuit design and measurement strategy are both assessed, so understanding the method at a conceptual level — not just memorising steps — is essential.

One design decision worth understanding: a potential divider circuit (rather than a simple variable resistor in series) allows the voltage across the component to be varied continuously from 0 V, which gives a more complete characteristic curve. A series variable resistor cannot reduce the voltage to zero, so it misses the low-voltage region of the graph.

8. Ideal Ammeters and Voltmeters

AQA specifies that unless a question states otherwise, you should treat ammeters as ideal — meaning they have zero resistance — and voltmeters as ideal — meaning they have infinite resistance. This simplifies circuit analysis considerably.

The reasoning is straightforward. An ammeter is placed in series, so any resistance it adds would reduce the current being measured and introduce error. Zero resistance means it has no effect on the circuit. A voltmeter is placed in parallel, so any current it draws would alter the current through the component being measured. Infinite resistance means it draws no current and leaves the circuit undisturbed.

In practice, real ammeters have a small but non-zero resistance, and real voltmeters have a large but finite resistance. For most A-level calculations, the ideal assumption is valid and expected. If a question provides the internal resistance of a metre, that is a signal to account for it explicitly — but only then.

9. Comparing the Three Components: A Summary

Before moving to exam technique, it is worth consolidating the three characteristics side by side. The differences in graph shape, resistance behaviour, and physical explanation are all fair game for 'compare' and 'explain' questions.

10. Exam Technique: Securing Every Mark

I-V characteristic questions appear in several formats: graph sketching, graph reading, calculation, and extended explanation. Each format has its own mark-winning strategy.

For graph sketching: the ohmic conductor must pass through the origin with a constant gradient. The filament lamp must pass through the origin but with a gradient that decreases symmetrically on both sides. The diode must show negligible current for negative voltages and a sharp upward curve starting near +0.6 V. Examiners award marks for correct shape, correct symmetry (or asymmetry), and correct origin behaviour.

For explain questions about the filament lamp: the mark scheme typically requires you to link current → temperature → ion vibration → increased collision frequency → increased resistance. Missing any link in this chain loses marks. Saying 'resistance increases because it gets hotter' earns partial credit at best; the full chain earns full credit.

For axis-orientation questions: before reading any gradient or trend, check which quantity is on which axis. If $I$ is on the horizontal axis and $V$ is on the vertical axis, a steeper gradient means higher resistance (gradient = $R$), which is the opposite conclusion from the more common orientation. Writing 'gradient = $R$' or 'gradient = $1/R$' explicitly in your working signals to the examiner that you have identified the axis convention correctly.

Across all three components, the underlying thread is the same: the I-V graph shape directly encodes how resistance behaves. A straight line means constant resistance (ohmic); a curve bending towards the voltage axis means increasing resistance; an asymmetric shape means fundamentally different behaviour in each direction. Recognising these patterns and explaining them in terms of physical mechanisms is the core skill this topic tests.