electrical resistance

The electrical resistance of an object is a measure of its opposition to the flow of electric current. Its reciprocal quantity is electrical conductance, measuring the ease with which an electric current passes. Electrical resistance shares some conceptual parallels with mechanical friction. The SI unit of electrical resistance is the ohm (Ω), while electrical conductance is measured in siemens (S) (formerly called the 'mho' and then represented by ℧).

Electric resistance
Common symbols	R
SI unit	ohm (Ω)
In SI base units	kg⋅m2⋅s−3⋅A−2
Dimension	${\displaystyle {\mathsf {M}}{\mathsf {L}}^{2}{\mathsf {T}}^{-3}{\mathsf {I}}^{-2}}$

Electric conductance
Common symbols	G
SI unit	siemens (S)
In SI base units	kg−1⋅m−2⋅s3⋅A2
Derivations from other quantities	${\displaystyle G={\frac {1}{R}}}$
Dimension	${\displaystyle {\mathsf {M}}^{-1}{\mathsf {L}}^{-2}{\mathsf {T}}^{3}{\mathsf {I}}^{2}}$

The resistance of an object depends in large part on the material it is made of. Objects made of electrical insulators like rubber tend to have very high resistance and low conductance, while objects made of electrical conductors like metals tend to have very low resistance and high conductance. This relationship is quantified by resistivity or conductivity. The nature of a material is not the only factor in resistance and conductance, however; it also depends on the size and shape of an object because these properties are extensive rather than intensive. For example, a wire's resistance is higher if it is long and thin, and lower if it is short and thick. All objects resist electrical current, except for superconductors, which have a resistance of zero.

The resistance R of an object is defined as the ratio of voltage V across it to current I through it, while the conductance G is the reciprocal: $${\displaystyle R={\frac {V}{I}},\qquad G={\frac {I}{V}}={\frac {1}{R}}.}$$

For a wide variety of materials and conditions, V and I are directly proportional to each other, and therefore R and G are constants (although they will depend on the size and shape of the object, the material it is made of, and other factors like temperature or strain). This proportionality is called Ohm's law, and materials that satisfy it are called ohmic materials.

In other cases, such as a transformer, diode or battery, V and I are not directly proportional. The ratio ⁠V/I⁠ is sometimes still useful, and is referred to as a chordal resistance or static resistance, since it corresponds to the inverse slope of a chord between the origin and an I–V curve. In other situations, the derivative ${\textstyle {\frac {\mathrm {d} V}{\mathrm {d} I}}}$ may be most useful; this is called the differential resistance.