When electric current flows through a metal wire or through other circuit elements, it encounters a certain amount of resistance, the magnitude of which depends on the electrical properties of the material.

practically all circuit elements exhibit some resistance; as a consequence, current flowing through an element will cause energy to be dissipated in the form of heat. An ideal resistor is a device that exhibits linear resistance properties according to Ohm’s law, which states that

V = IR Ohm’s law

The resistance of a material depends on a property called resistivity, denoted by the symbol ρ ; the inverse of resistivity is called conductivity and is denoted by the symbol σ . For a cylindrical resistance element , the resistance is proportional to the length of the sample l and inversely proportional to its crosssectional area A and conductivity σ.

Ohm’s law is an empirical relationship that finds widespread application in electrical engineering because of its simplicity. It is, however, only an approximation of the physics of electrically conducting materials.

In addition to the resistance in ohms, the maximum allowable power dissipation (or power rating) is typically specified for commercial resistors. Exceeding this power rating leads to overheating and can cause the resistor to literally burn up. For a resistor R, the power dissipated can be expressed, with Ohm’s law substituted into equation