Why Is Capacitor Reactance 1/LC Instead of 1/sqrt(LC)?

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Homework Help Overview

The discussion revolves around the reactance of capacitors in the context of electrical circuits, specifically questioning the expression for reactance and its relationship to frequency and capacitance.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are exploring the correct expression for capacitor reactance and questioning the validity of various forms, including 1/LC and 1/((2πf)^2)C. There is a focus on understanding the implications of these expressions in terms of units and physical meaning.

Discussion Status

The discussion is ongoing, with participants providing insights into the definitions and relationships between frequency, capacitance, and reactance. Some have offered unit analysis as a method to clarify the concepts involved.

Contextual Notes

There appears to be some confusion regarding the correct formula for capacitor reactance and its derivation, with participants questioning assumptions about the relationships between the variables involved.

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Homework Statement


I just want to know why the reactance of a capacitor is 1/LC rather than 1/[tex]\sqrt{}LC[/tex]?


Homework Equations


2(pi)f = 1/sqrt(LC)
 
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ben.tien said:

Homework Statement


I just want to know why the reactance of a capacitor is 1/LC rather than 1/[tex]\sqrt{}LC[/tex]?

It's not. The magnitude of the reactance of a capacitor C is 1/(2πfC). Or, treating it as a complex impedance, the impedance is 1/(j2πfC).
 
gneill said:
It's not. The magnitude of the reactance of a capacitor C is 1/(2πfC). Or, treating it as a complex impedance, the impedance is 1/(j2πfC).

yeah my bad why is it that instead of 1/((2pif)^2)C)
 
ben.tien said:
yeah my bad why is it that instead of 1/((2pif)^2)C)

You can do a unit analysis. Capacitance is Coulombs per volt. So, ignoring unitless constants,

1/(f*C) ==> [T][V]/[Q]

but amps is charge per unit time, or [A] = [Q]/[T], so our units become

[T][V]/[Q] ==> [V]/[A] ==> Ohms.
 

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