Ohmic and Nonohmic Circuit Elements

Ohm's law, V = IR, holds perfectly only for components whose resistance stays fixed no matter what voltage you apply. Plot current against voltage for one of these and you get a straight line through the origin, with the slope giving you 1/R. A plain resistor behaves this way across a huge range of conditions, which is why it is the default example whenever a circuit problem wants clean, predictable numbers.

A filament light bulb breaks that pattern. Push more voltage across it, more current flows, and that current heats the metal filament. A hotter metal lattice vibrates more violently, and those vibrations scatter the drifting electrons more often, so the filament's own resistance climbs as it gets brighter. The result is a curve that bends over, rising less steeply at high voltage than at low voltage, because each extra volt now fights a bigger resistance. A diode goes further still: it conducts almost nothing in one direction and then lets current rise sharply once voltage passes a threshold in the other, giving a curve that is flat, then steep.

None of this means the measurement is broken. A curved I-V graph is data telling you the truth about a real component: its resistance is not constant, it depends on conditions like temperature or voltage direction. This sits right next to the idea of power dissipation in circuits, since a filament's changing resistance also changes how much power it burns as it heats up, and it sets up diodes and other nonlinear devices you meet when circuits stop being simple resistor networks.