Electrical resistivity and conductivity ions. In biological membranes, currents are carried by ionic salts. Small holes in cell membranes, called ion channels, are selective to specific ions and determine the membrane resistance. The electrical resistivity of a metallic conductor decreases gradually as temperature is lowered. In ordinary conductors, such as copper or silver, this decrease is limited by impurities and other defects. Even near absolute zero, a real sample of a normal conductor shows some resistance. In a superconductor, the resistance drops abruptly to zero when the material is cooled below its critical temperature. An electric current flowing in a loop of superconducting wire
Electrical resistivity and conductivity individual matrix elements are not necessarily reciprocals of one another; for example, "σ" may not be equal to 1/"ρ". This can be seen in the Hall effect, where formula_34 is nonzero. In the Hall effect, due to rotational invariance about the z-axis, formula_35 and formula_36, so the relation between resistivity and conductivity simplifies to: If the electric field is parallel to the applied current, formula_34 and formula_40 are zero. When they are zero, one number, formula_41, is enough to describe the electrical resistivity. It is then written as simply formula_9, and this reduces to the simpler expression. According to elementary