Quick question about reactance

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In summary, there is confusion regarding the definition of reactance and the correct notation. While some sources define reactance as the magnitude of the complex part of impedance, others define it as the magnitude of impedance itself. It is important to clarify the correct definition before using it in equations. Additionally, the phase of a perfect inductor or capacitor is always ±π/2 due to the fact that the resistance is zero, resulting in an undefined arctan value.
  • #1
JesseC
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My notes say reactance is the magnitude of impedance, so I assume it means this:

[tex] |Z| = \sqrt{X^2 + Y^2} [/tex]

but this is contradicted by numerous internet sources I've read which say that it is the magnitude of the complex part of impedance [tex] |Y| [/tex] . Could someone clarify this?

I'm more inclined to trust the internet given my lecturer is an Astronomer :P
 
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  • #2
JesseC said:
My notes say reactance is the magnitude of impedance, so I assume it means this:

[tex] |Z| = \sqrt{X^2 + Y^2} [/tex]

but this is contradicted by numerous internet sources I've read which say that it is the magnitude of the complex part of impedance [tex] |Y| [/tex] . Could someone clarify this?

I'm more inclined to trust the internet given my lecturer is an Astronomer :P

The following is the correct form. R is resistance, & X is reactance. BTW, "Y" is admittance, the reciprocal of impedance. Did I help?

[tex] |Z| = \sqrt{R^2 + X^2} [/tex]

Claude
 
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  • #3
Yeah sorry, I've used confusing notation such that Z being a complex number was of the form Z = X+Yj. So the real part X is resistance, and the imaginary part Y is reactance. Clearly modulus of Z is something else altogether, what would its use be?

I have another question while I'm here: Is the phase of a perfect inductor or capacitor always +π/2 or -π/2?

Given that (using your notation) phase is arctan(X/R) and for a capacitor or inductor R = 0, then ±π/2 = arctan(±∞). I never trust myself when it comes to things involving circuits.
 

1. What is reactance?

Reactance is a measure of a circuit element's opposition to the flow of alternating current (AC). It is measured in ohms and is represented by the symbol X.

2. How is reactance different from resistance?

Reactance and resistance are both components of impedance, which measures the overall opposition to current flow in a circuit. The main difference is that resistance refers to the opposition to direct current (DC) while reactance refers to the opposition to AC.

3. What are the two types of reactance?

The two types of reactance are capacitive reactance (Xc) and inductive reactance (Xl). Capacitive reactance is caused by capacitors and opposes the flow of current in a circuit, while inductive reactance is caused by inductors and opposes changes in the flow of current.

4. How is reactance calculated?

The reactance of a circuit element can be calculated using the formula X = 1/(2πfC) for capacitive reactance and X = 2πfL for inductive reactance, where f is the frequency of the AC and C or L is the capacitance or inductance of the element, respectively.

5. What are some practical applications of reactance?

Reactance is an important concept in the design and analysis of electrical circuits. It is used in the design of filters, impedance matching networks, and other circuit components. It is also important in understanding the behavior of AC circuits and in troubleshooting problems in electronic devices.

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