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The telegrapher's equations then describe the relationship between the voltage V and the current I along the transmission line, each of which is a function of position x and time t: = (,) = (,) The equations themselves consist of a pair of coupled, first-order, partial differential equations. The first equation shows that the induced voltage is ...
The telegrapher's equations (or just telegraph equations) are a pair of linear differential equations which describe the voltage and current on an electrical transmission line with distance and time. They were developed by Oliver Heaviside who created the transmission line model , and are based on Maxwell's equations .
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.
In physics, there are equations in every field to relate physical quantities to each other and perform calculations. Entire handbooks of equations can only summarize most of the full subject, else are highly specialized within a certain field. Physics is derived of formulae only.
The source free equations can be written by the action of the exterior derivative on this 2-form. But for the equations with source terms (Gauss's law and the Ampère-Maxwell equation), the Hodge dual of this 2-form is needed. The Hodge star operator takes a p-form to a (n − p)-form, where n is the number of dimensions.
Symbol Meaning SI unit of measure magnetic vector potential: tesla meter (T⋅m) : area: square meter (m 2) : amplitude: meter: atomic mass number: unitless acceleration: meter per second squared (m/s 2)
The solutions to the long line transmission equations include incident and reflected portions of the voltage and current: = + + = / + / When the line is terminated with its characteristic impedance, the reflected portions of these equations are reduced to 0 and the solutions to the voltage and current along the transmission line are wholly ...
The phase velocity at which electrical signals travel along a transmission line or other cable depends on the construction of the line. Therefore, the wavelength corresponding to a given frequency varies in different types of lines, thus at a given frequency different conductors of the same physical length can have different electrical lengths.