Find the true statement:

The correct answer is Option (4) → Resistance of carbon decreases with the increase of temperature.

Each statement is judged against the behaviour of the material or device it names.

Option (1) Ohm's law is applicable to diode — Incorrect. A diode is a non-ohmic device: its current is not proportional to the voltage across it, and it conducts in one direction only.

Option (2) Resistance of an incandescent lamp decreases when it is switched on — Incorrect. The tungsten filament heats up to a very high temperature, and the resistance of a metal increases with temperature. So the resistance of the lamp rises after switching on.

Option (3) Resistivity of a wire depends on its dimensions — Incorrect. Resistivity is a property of the material (and of temperature). It is the resistance, \( R = \rho l/A \), that depends on the length and the area.

Option (4) Resistance of carbon decreases with the increase of temperature — Correct. Carbon behaves like a semiconductor: the number of free charge carriers increases with temperature, which more than makes up for the more frequent collisions, so its resistance falls (it has a negative temperature coefficient).