Electric effective resistance

"Electric effective resistance" is the parameter of a passive two-pole electric circuit or its element, which is equal to the relation of the effective power, which is absorbing in this element, to the square of the effective value of an electric current in it.

Electric effective resistance is the component of complex electric impedance of the alternating current circuit, which absorbs an electric energy, and can be determined by calculation in function of the active power $P$ and the effective value of an electric current $I$ accordingly to the formula: $r\; =\; frac\{P\}\{I^2\}$. This effective resistance has the larger value, than action resistance to a direct current, in consequence of a non-uniform distribution of an alternating current in the cross-section of a conductor owing to the surface effect. For a low frequency (the power frequency in 50 – 60 Hz) the effective resistance of the copper wires with the diameter up to 1 centimetre is practically equal to an ohm resistance. In effective resistance the part of energy loss is producing by the loss in its magnetic and electric fields. The electric effective resistance on a complex plane appears as the side of the resistance triangle for electric circuit of an alternating current. The effective electric resistance is bounding with the effective electric conductance $g$ by the expression :$g\; =\; frac\{r\}\{z^2\}$

where $z$ is the full electric impedance of an electric circuit.

References

[1] Pohl R. W. ELEKTRIZITÄTSLEHRE. – Berlin-Gottingen-Heidelberg: SPRINGER-VERLAG, 1960.

[2] Popov V. P. The Principles of Theory of Circuits. – M.: Higher School, 1985, 496 p. (In Russian).

[3] Küpfmüller K. Einführung in die theoretische Elektrotechnik, Springer-Verlag, 1959.