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Current-voltage characteristics
Put a component through its paces, plotting current against pd, and the shape of the graph is the component's fingerprint. Three fingerprints are required, and only one of them obeys Ohm's law.
Builds on Current, charge and the direction problem.
IN THIS TOPIC
- Sketch and interpret the I-V characteristics of an ohmic conductor, a filament lamp and a semiconductor diode.
- State Ohm's law as the special case I ∝ V under constant physical conditions.
- Read resistance from a characteristic as the ratio V/I at a point, never as a gradient of a curve.
WHAT YOU PROBABLY THINK
Ohm's law applies to everything.
Taking a component's portrait
The characteristic is measured with a simple circuit: vary the pd across the component, record the current through it, and plot one against the other. Unless a question says otherwise, the meters are treated as ideal: the ammeter has zero resistance and the voltmeter infinite, so neither disturbs what it measures.
One small trap in the plotting itself: AQA allows either quantity on the horizontal axis. The same component's fingerprint looks reflected when the axes swap, so read the axis labels before reading the shape.
The ohmic conductor
A metal wire at constant temperature gives the simplest possible fingerprint: a straight line through the origin.
This is Ohm's law: current is proportional to pd, I ∝ V, provided physical conditions stay constant. That proviso is the law's whole content. Ohm's law is not a universal rule of circuits; it is the name for the special case in which the ratio V/I happens to stay fixed, and the next two components break it openly.
The filament lamp
A lamp's filament runs white-hot, and the current itself does the heating. More current means a hotter filament, whose metal ions vibrate more violently, obstructing the charge carriers more often: the resistance rises with the current.
The graph shows exactly that: steep near the origin where the filament is coolest, flattening as V grows and the heating bites. The curve is symmetric through the origin, because the filament neither knows nor cares which way the current runs.
The diode
A semiconductor diode is a one-way valve. In reverse, and in forward bias below a threshold pd of about 0.6 V, it passes almost no current; beyond the threshold the current rises very steeply for tiny increases in pd.
Reading resistance from the graph
At any point on any characteristic, the resistance is the definition doing its job: R = V/I, the ratio of the coordinates at that point. On the ohmic line the ratio is the same everywhere, which is what makes it ohmic. On the lamp's curve the ratio grows as you move out along it.
What resistance is not is the gradient of a curved characteristic. The tangent's slope at a point on the lamp curve is a genuine quantity, but it is not V/I there, and quoting it as the resistance is one of the most reliably punished errors in the unit. Ratio of coordinates, every time.
THE EXAM BIT
- Resistance from a characteristic is the ratio V/I at the point, never the tangent's gradient. On a curve the two differ, and the mark scheme knows it.
- The lamp explanation is a chain, in order: current heats the filament; the ions vibrate with larger amplitude; charge carriers collide with them more frequently; resistance rises. Each link scores.
- Quote Ohm's law with its condition: I ∝ V provided physical conditions, principally temperature, remain constant. The condition is the mark.
- Check which axis is which before describing a shape: with V on the vertical axis every fingerprint reflects, and the diode's steep rise becomes a flat run.
- Ideal meters are the default: ammeter resistance zero, voltmeter infinite. Only depart from that when the question does.
CHECK YOURSELF
From a filament lamp's characteristic: at 2.0 V the current is 0.50 A, and at 12 V it is 1.5 A. Find the resistance at each point, and explain the change.
Show a hint
Resistance is a ratio of coordinates, taken twice.
Show the answer
At 2.0 V: R = V/I = 2.0 / 0.50 = 4.0 Ω. At 12 V: R = 12 / 1.5 = 8.0 Ω.
The resistance has doubled because the larger current runs the filament far hotter: its ions vibrate more, the carriers collide with them more often, and the same pd drives proportionally less current.
R is the ratio V over I.
Never the gradient of a curve.
No animated video for this topic yet; these notes stand alone. InkPhysics on YouTube.