One proposal was to devise a unit based on a mercury column that would be coherent – in effect, adjusting the length to make the resistance one ohm. However, this unit was not coherent with other units. He proposed a column of pure mercury, of one square millimeter cross section, one metre long: Siemens mercury unit. In 1860 Werner Siemens (1816–1892) published a suggestion for a reproducible resistance standard in Poggendorffs Annalen der Physik und Chemie. Various artifact standards were proposed as the definition of the unit of resistance. However, the centimeter-gram-second, CGS, units turned out to have impractical sizes for practical measurements. These units had the great advantage of simplifying the equations used in the solution of electromagnetic problems, and eliminated conversion factors in calculations about electrical quantities. The absolute-units system related magnetic and electrostatic quantities to metric base units of mass, time, and length. Some early definitions of a unit of resistance, for example, defined a unit resistance as one quadrant of the Earth per second. Since so-called "absolute" units of charge and current are expressed as combinations of units of mass, length, and time, dimensional analysis of the relations between potential, current, and resistance show that resistance is expressed in units of length per time – a velocity. It is desirable that one unit of electrical potential will force one unit of electric current through one unit of electrical resistance, doing one unit of work in one unit of time, otherwise, all electrical calculations will require conversion factors. Defining a unit for resistance that is coherent with units of energy and time in effect also requires defining units for potential and current. This latter method ensures coherence with the units of energy. Alternatively, the electrical units can be related to the mechanical units by defining, for example, a unit of current that gives a specified force between two wires, or a unit of charge that gives a unit of force between two unit charges. Various artifacts, such as a length of wire or a standard electrochemical cell, could be specified as producing defined quantities for resistance, voltage, and so on. Two different methods of establishing a system of electrical units can be chosen. Electrical units so defined were not a coherent system with the units for energy, mass, length, and time, requiring conversion factors to be used in calculations relating energy or power to resistance. Resistance was often expressed as a multiple of the resistance of a standard length of telegraph wires different agencies used different bases for a standard, so units were not readily interchangeable. Telegraphers and other early users of electricity in the 19th century needed a practical standard unit of measurement for resistance. The rapid rise of electrotechnology in the last half of the 19th century created a demand for a rational, coherent, consistent, and international system of units for electrical quantities. Since the ohm belongs to a coherent system of units, when each of these quantities has its corresponding SI unit ( watt for P, ohm for R, volt for V and ampere for I, which are related as in § Definition, this formula remains valid numerically when these units are used (and thought of as being cancelled or omitted). Where alternating current is applied to the circuit (or where the resistance value is a function of time), the relation above is true at any instant but calculation of average power over an interval of time requires integration of "instantaneous" power over that interval. Non-linear resistors have a value that may vary depending on the applied voltage (or current). P is the power R is the resistance V is the voltage across the resistor I is the current through the resistorĪ linear resistor has a constant resistance value over all applied voltages or currents many practical resistors are linear over a useful range of currents. Ω = V A = 1 S = W A 2 = V 2 W = s F = H s = J ⋅ s C 2 = kg ⋅ m 2 s ⋅ C 2 = J s ⋅ A 2 = kg ⋅ m 2 s 3 ⋅ A 2 The ohm is defined as an electrical resistance between two points of a conductor when a constant potential difference of one volt, applied to these points, produces in the conductor a current of one ampere, the conductor not being the seat of any electromotive force. One of the functions of many types of multimeters is the measurement of resistance in ohms.
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