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

[ben.tien]

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)

 

[gneill]

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).

 

[ben.tien]

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)

 

[gneill]

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.