Resistors are fundamental components in electrical circuits, often manufactured from metallic alloys or carbon compounds. They model a material's ability to resist the flow of electric current, a characteristic that is crucial in controlling and regulating electrical power within a circuit.

This current-resisting behavior of resistors is governed by Ohm's law, which states that the voltage across a resistor is directly proportional to the current flowing through it.

The constant of proportionality in this relationship is known as resistance. Measured in units called ohms (Ω), resistance indicates how effectively a material can impede the flow of electric current.

The resistance of a material is directly proportional to its length and inversely proportional to its cross-sectional area. The proportionality constant in this relationship is known as resistivity, which varies among different materials. Conductors, which allow easy passage of electrical current, have low resistivities, while insulators, which block the flow of current, have high resistivities.

Resistors can further be categorized into linear and non-linear based on their voltage-current relationship. Linear resistors obey Ohm's law, exhibiting a linear relationship between their current and voltage. Non-linear resistors, on the other hand, do not adhere to this law, and their resistance changes with the applied voltage or current.

Two extreme cases of resistance are short circuits and open circuits. A short circuit has zero resistance and voltage drop, allowing it to carry any amount of current. In contrast, an open circuit has infinite resistance, resulting in zero current flow, and can sustain an unrestricted voltage.

Conversely, the reciprocal of resistance is known as conductance. This measures how well an element conducts electric current. Conductance is measured in Siemens (S), with one Siemens being equivalent to one ampere per volt.