Question

To understand the concept of reactance (of an inductor) and its frequency dependence.

When an inductor is connected to a voltage source that varies sinusoidally, a sinusoidal current will flow through the inductor, its magnitude depending on the frequency. This is the essence of AC (alternating current) circuits used in radio, TV, and stereos. Circuit elements like inductors, capacitors, and resistors are linear devices, so the amplitude I0 of the current will be proportional to the amplitude V0 of the voltage. However, the current and voltage may not be in phase with each other. This new relationship between voltage and current is summarized by the reactance, the ratio of voltage and current amplitudes, V0, and I0: XL=V0/I0, where the subscript L indicates that this formula applies to an inductor.

What is the reactance XL of an inductor?

Answer 1

Z2=jXL
Z3=-jXc

Z12 = Z1 || Z2 = Z1*Z2/(Z1+Z2) (this is parallel connection)
Z12 = jXL *R/ (R+jXL)
Z12 = jXL *R * (R- jXL) / (R^2+ XL^2)

In electrical and electronic systems, reactance is the opposition of a circuit element to a change of electric current or voltage, due to that element's inductance or capacitance. A built-up electric field resists the change of voltage on the element, while a magnetic field resists the change of current. The notion of reactance is similar to electrical resistance, but they differ in several respects.

An ideal resistor has zero reactance, while ideal inductors and capacitors consist entirely of reactance, having zero resistance.

Z= Z12 + Z3 (this is series connection)
Z= jXL *R * (R- jXL) / (R^2+ XL^2) -jXc
Z= jXL *R * (R- jXL) / (R^2+ XL^2) -jXc*(R^2+ XL^2)/ (R^2+ XL^2)
Z= [jXL *R * (R- jXL) -jXc*(R^2+ XL^2) ]/ (R^2+ XL^2)
Z= [jXL*R^2 + XL^2 - jXc*R^2- jXc*XL^2] / (R^2+ XL^2)

Note that |Z|=sqrt(Re{Z}^2 + Im{Z}^2)