Reactance and Impedence

  • Thread starter ben.tien
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  • #1
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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)
 

Answers and Replies

  • #2
gneill
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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]?

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).
 
  • #3
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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)
 
  • #4
gneill
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2,867
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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