Current-voltage characteristics

Taking a component's portrait

The circuit is simple enough. Vary the pd across the component, record the current through it, plot one against the other. Unless a question says otherwise the meters are ideal, meaning zero resistance in the ammeter and infinite resistance in the voltmeter, so neither disturbs what it is there to measure.

There is a small trap in the plotting itself. Exam papers put either quantity on the horizontal axis, and the same component's curve looks reflected when the axes swap. Read the axis labels before you read the shape.

The ohmic conductor

A metal wire held at constant temperature gives the simplest characteristic of all, a straight line through the origin.

That straight line is Ohm's law. Current is proportional to pd, I ∝ V, provided physical conditions stay constant, and the proviso carries the law's whole content. Treat the law as the name for one well-behaved special case, the case where V/I happens to stay fixed. Plenty of components ignore it, and the next two 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, so the resistance rises with the current.

The graph shows exactly that. Steep near the origin, where the filament is coolest, then flattening as V grows and the heating bites. Symmetry through the origin comes for free, since the filament behaves the same way whichever 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 climbs very steeply for tiny increases in pd. The arrow in the circuit symbol points the way conventional current is allowed through, and getting that arrow round the wrong way is what invalidates a sketched circuit.

Reading resistance from the graph

At any point on any characteristic the definition still applies. R = V/I, the ratio of the two coordinates at that point. Along the ohmic line that ratio comes out the same everywhere, which is what ohmic means. Along the lamp's curve it grows as you move outwards.

Now the error that costs more marks than any other in this unit. On a curve, the gradient of the tangent and the ratio V/I are two different numbers, and only the ratio gives the resistance. The tangent slope has a genuine meaning of its own, but write it down as the resistance and the mark is gone. Coordinates, every time.