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In electrical engineering, electrical length is a dimensionless parameter equal to the physical length of an electrical conductor such as a cable or wire, divided by the wavelength of alternating current at a given frequency traveling through the conductor. [1] [2] [3] In other words, it is the length of the conductor measured in wavelengths.
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 electrical resistance of a uniform conductor is given in terms of resistivity by: [40] = where ℓ is the length of the conductor in SI units of meters, a is the cross-sectional area (for a round wire a = πr 2 if r is radius) in units of meters squared, and ρ is the resistivity in units of ohm·meters.
The resistivity can be expressed using the SI unit ohm metre (Ω⋅m) — i.e. ohms multiplied by square metres (for the cross-sectional area) then divided by metres (for the length). Both resistance and resistivity describe how difficult it is to make electrical current flow through a material, but unlike resistance, resistivity is an ...
The resistance of copper wire is approximately 1 ohms / 1000 feet for 10 AWG, 10 ohms / 1000 feet for 20 AWG, 100 ohms / 1000 feet for 30 AWG, and so on. [ 5 ] : 27 Because aluminum wire has a conductivity of approximately 61% of copper, an aluminum wire has nearly the same resistance as a copper wire that is two sizes ...
At a distance x into the line, there is current phasor I(x) traveling through each wire, and there is a voltage difference phasor V(x) between the wires (bottom voltage minus top voltage). If Z 0 {\displaystyle Z_{0}} is the characteristic impedance of the line, then V ( x ) / I ( x ) = Z 0 {\displaystyle V(x)/I(x)=Z_{0}} for a wave moving ...
The typical digital propagation delay of a resistive wire is about half of R times C; since both R and C are proportional to wire length, the delay scales as the square of wire length. Charge spreads by diffusion in such a wire, as explained by Lord Kelvin in the mid nineteenth century. [ 2 ]
The unit was based upon the ohm equal to 10 9 units of resistance of the C.G.S. system of electromagnetic units. The international ohm is represented by the resistance offered to an unvarying electric current in a mercury column of constant cross-sectional area 106.3 cm long of mass 14.4521 grams and 0 °C.