Ohm's Law is the relationship between the potential difference applied across an electrical conductor and the current flowing in the conductor. This relationship is
where R is the electrical resistance, the constant of proportionality.
The unit of resistance is the ohm, Ω, that being the resistance between two points of a conductor when a potential difference of 1 volt, produces a current of 1 amp between the two points. An alternate definition of the ohm is the resistance of conductor in which a current of 1 amp generates heat at the rate of 1 watt, i.e.,
The reciprocal of resistance is called the conductance, G; the unit of conductance is the siemen, S. The resistance, and thus conductance, depend upon the material, the cross-section, s, and the length, l, of the conductor. When the resistance is calculated on the basis of unit length and unit cross-section, the quantity called resistivity, ρ, is defined
The inverse of the resistivity is the conductivity, κ = l/ρ. For solid substances and single component liquids, resistivity is a characteristic of a particular substance. A highly conducting solid such as copper has a resistivity of 1.725 × 10−8 Ωm (at 20°C) whereas a poorer conducting solid, such as carbon has a resistivity of 7.10−6 Ωm.
The resistivity of all pure metals increases with temperature whereas the resistivity of carbon, insulating materials and electrolytes decreases with temperature. The resistance of electrolytes depends largely on the ionic components and their concentrations in solution. Generally over moderate concentration ranges, resistivity decreases with increasing concentration but reaches a minimum value at a particular, moderately high concentration. For example, aqueous solutions of sodium hydroxide have minimum restivities at a concentration of approximately 6 kmol m−3 (at approximately 20°C).
Heat & Mass Transfer, and Fluids Engineering