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

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The reactance of a capacitor is defined as 1/(2πfC), not 1/LC or 1/√(LC). This formula arises from the relationship between frequency and capacitance in AC circuits. When analyzing units, capacitance is expressed in Coulombs per volt, leading to the conclusion that reactance has units of ohms. The discussion clarifies that the correct formulation for capacitive reactance incorporates frequency, emphasizing the importance of understanding complex impedance. Overall, the confusion stems from misinterpretation of the reactance formula in relation to frequency and capacitance.
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Homework Statement


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


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/\sqrt{}LC?

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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