Ohm's law and I-V characteristics

The main symbols used in this lesson:

Ohm's law is a statement about one kind of conductor under one condition. It says the current through a metallic conductor is directly proportional to the potential difference across it, provided its temperature stays constant (and the other physical conditions - length, cross-sectional area, material - do not change).

So for an ohmic conductor:

$I \propto V \quad\Longleftrightarrow\quad V = IR \text{ with } R \text{ constant}$

The graph of $I$ against $V$ is a straight line through the origin. Double the p.d. and you double the current.

Two things students get wrong here:

1. Ohm's law is not the definition of resistance. $R = V/I$ defines resistance and works for every component, ohmic or not. Ohm's law is the extra claim that for a metallic conductor at constant temperature, that ratio $R$ happens to be the same at every point on the characteristic.
2. It is not a law of nature that applies to everything. A filament lamp, a diode and a thermistor all disobey it. Even a metal wire obeys it only while its temperature is held constant - pass a large enough current and the wire heats up, and its $R$ changes.

Because Ohm's law is usually tested as a statement to recall, learn it with the condition attached. "Current is proportional to p.d." alone is not a complete answer.