The ohm (symbol: Ω, the uppercase Greek letter omega) is the unit of electrical resistance in the International System of Units (SI). It is named after German physicist Georg Ohm (1789–1854). Various empirically derived standard units for electrical resistance were developed in connection with early telegraphy practice, and the British Association for the Advancement of Science proposed a unit derived from existing units of mass, length and time, and of a convenient scale for practical work as early as 1861. Following the 2019 revision of the SI, in which the ampere and the kilogram were redefined in terms of fundamental constants, the ohm is now also defined as an exact value in terms of these constants.
Definition The ohm is defined as an electrical resistance between two points of a conductor when a constant potential difference of one volt (V), applied to these points, produces in the conductor a current of one ampere (A), the conductor not being the seat of any electromotive force.
Ω = V A = 1 S = W A 2 = V 2 W = s F = H s = W b C = J ⋅ s C 2 = J s ⋅ A 2 = k g ⋅ m 2 s ⋅ C 2 = k g ⋅ m 2 s 3 ⋅ A 2 {\displaystyle \Omega ={\frac {\mathrm {V} }{\mathrm {A} }}={\frac {1}{\mathrm {S} }}={\frac {\mathrm {W} }{\mathrm {A^{2}} }}={\frac {\mathrm {V} ^{2}}{\mathrm {W} }}={\frac {\mathrm {s} }{\mathrm {F} }}={\frac {\mathrm {H} }{\mathrm {s} }}={\frac {\mathrm {Wb} }{\mathrm {C} }}={\frac {\mathrm {J{\cdot }s} }{\mathrm {C^{2}} }}={\frac {\mathrm {J} }{\mathrm {s{\cdot }A^{2}} }}={\frac {\mathrm {kg{\cdot }m^{2}} }{\mathrm {s{\cdot }C^{2}} }}={\frac {\mathrm {kg{\cdot }m^{2}} }{\mathrm {s^{3}{\cdot }A^{2}} }}}
In many cases the resistance of a conductor is approximately constant within a certain range of voltages, temperatures, and other parameters. These are called linear resistors. In other cases resistance varies, such as in the case of the thermistor, which exhibits a strong dependence of its resistance with temperature.
In the US, consecutive vowels in the prefixed units "kiloohm" and "megaohm" are commonly reduced to one, producing "kilohm" and "megohm". In alternating current circuits, electrical impedance is also measured in ohms.
Relation to conductance The siemens (S) is the SI derived unit of electric conductance and admittance, historically known as the "mho" (ohm spelled backwards, symbol is ℧); it is one reciprocal ohm: 1 S = 1 Ω−1.
Power as a function of resistance The power dissipated by a resistor may be calculated from its resistance, and the voltage or current involved. The formula is a combination of Ohm's law and Joule's law:
P = V I = V 2 R = I 2 R , {\displaystyle P=VI={\frac {V^{2}}{R}}=I^{2}R,}
where P is the power, R is the resistance, V is the voltage across the resistor, and I is the current through the resistor. A linear resistor has a constant resistance value over all applied voltages or currents; many practical resistors are linear over a useful range of currents. Non-linear resistors have a value that may vary depending on the applied voltage (or current). 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. 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).
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