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Ohm's law has been observed on a wide range of length scales. In the early 20th century, it was thought that Ohm's law would fail at the atomic scale, but experiments have not borne out this expectation. As of 2012, researchers have demonstrated that Ohm's law works for silicon wires as small as four atoms wide and one atom high. [17]
The above equation can be transposed to get Pouillet's law (named after Claude Pouillet): R = ρ ℓ A . {\displaystyle R=\rho {\frac {\ell }{A}}.} The resistance of a given element is proportional to the length, but inversely proportional to the cross-sectional area.
The formula is a combination of Ohm's law and Joule's law: = = =, 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.
Ohm's law is satisfied when the graph is a straight line through the origin. Therefore, the two resistors are ohmic, but the diode and battery are not. For many materials, the current I through the material is proportional to the voltage V applied across it: over a wide range of voltages and currents. Therefore, the resistance and conductance ...
A Magic Triangle image mnemonic - when the terms of Ohm's law are arranged in this configuration, covering the unknown gives the formula in terms of the remaining parameters. It can be adapted to similar equations e.g. F = ma, v = fλ, E = mcΔT, V = π r 2 h and τ = rF sinθ.
A matrix version of Kirchhoff's current law is the basis of most circuit simulation software, such as SPICE. The current law is used with Ohm's law to perform nodal analysis. The current law is applicable to any lumped network irrespective of the nature of the network; whether unilateral or bilateral, active or passive, linear or non-linear.
In the case of resistive (Ohmic, or linear) loads, the power formula (P = I·V) and Joule's first law (P = I^2·R) can be combined with Ohm's law (V = I·R) to produce alternative expressions for the amount of power that is dissipated: ℘ = = = where R is the electrical resistance.
The two most significant results of the Drude model are an electronic equation of motion, = (+ ) , and a linear relationship between current density J and electric field E, =. Here t is the time, p is the average momentum per electron and q, n, m , and τ are respectively the electron charge, number density, mass, and mean free time between ...