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The SI unit of electrical resistivity is the ohm-metre (Ω⋅m). [ 1 ] [ 2 ] [ 3 ] For example, if a 1 m 3 solid cube of material has sheet contacts on two opposite faces, and the resistance between these contacts is 1 Ω , then the resistivity of the material is 1 Ω⋅m .
The siemens (symbol: S) is the unit of electric conductance, electric susceptance, and electric admittance in the International System of Units (SI). Conductance, susceptance, and admittance are the reciprocals of resistance, reactance, and impedance respectively; hence one siemens is equal to the reciprocal of one ohm (Ω −1) and is also referred to as the mho.
Conductivity or specific conductance of an electrolyte solution is a measure of its ability to conduct electricity. The SI unit of conductivity is siemens per meter (S/m). Conductivity measurements are used routinely in many industrial and environmental applications as a fast, inexpensive and reliable way of measuring the ionic content in a ...
where is the length of the conductor, measured in metres (m), A is the cross-sectional area of the conductor measured in square metres (m 2), σ is the electrical conductivity measured in siemens per meter (S·m −1), and ρ is the electrical resistivity (also called specific electrical resistance) of the material, measured in ohm-metres (Ω ...
The unit can be thought of as, loosely, "ohms · aspect ratio". Example: A 3-unit long by 1-unit wide (aspect ratio = 3) sheet made of material having a sheet resistance of 21 Ω/sq would measure 63 Ω (since it is composed of three 1-unit by 1-unit squares), if the 1-unit edges were attached to an ohmmeter that made contact entirely over each ...
where E is the electric field vector with units of volts per meter (analogous to V of Ohm's law which has units of volts), J is the current density vector with units of amperes per unit area (analogous to I of Ohm's law which has units of amperes), and ρ "rho" is the resistivity with units of ohm·meters (analogous to R of Ohm's law which has ...
j is the imaginary unit (i.e. j 2 = −1); and B is the real-valued susceptance, measured in siemens. The admittance ( Y ) is the reciprocal of the impedance ( Z ), if the impedance is not zero:
The units of specific contact resistivity are typically therefore in ohm-square metre, or Ω⋅m 2. When the current is a linear function of the voltage, the device is said to have ohmic contacts. Inductive and capacitive methods could be used in principle to measure an intrinsic impedance without the complication of contact resistance.