# Magnetic reactance

Magnetic reactance

Magnetic reactance is the parameter of a passive magnetic circuit or its element, which is equal to the square root of the difference of squares of the full and effective magnetic resistance for a magnetic current, taken with the sign plus, if the magnetic current lags behind the magnetic tension in phase, and with the sign minus, if the magnetic current leads the magnetic tension in phase.

Magnetic reactance [1-3] is the component of complex magnetic impedance of the alternating current circuit, which produces the phase shift between a magnetic current and magnetic tension in the circuit. It is measuring in units - [$\frac{1}{\Omega}$] and is denoting x (or X). It may be inductive xL = ωLM or capacitive $x_C = \frac{1}{\omega C_M}$, where ω is the angle frequency of a magnetic current, LM is the magnetic inductivity of a circuit, CM is the magnetic capacitivity of a circuit. The magnetic reactance of an undeveloped circuit with the inductivity and the capacitivity, which are connected in series, is equal: $x = x_L - x_C = \omega L_M - \frac{1}{\omega C_M}$ . If xL = xC, then the sum reactance x = 0 and in the circuit the resonance takes place. In the general case $x = \sqrt{z^2 - r^2}$. When an energy loss are absent (r = 0) x = z. The angle of the phase shift in a magnetic circuit $\phi = \arctan{\frac{x}{r}}$. On a complex plane the magnetic reactance appears as the side of the resistance triangle for circuit of an alternating current.

## 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.

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