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.

 

[rwisz]

(resonant frequency)

The reactance of a capacitor is not always 1/LC. It depends on the frequency of the applied voltage. At the resonant frequency, the reactance of a capacitor is indeed 1/\sqrt{}LC. However, at other frequencies, the reactance can be different. This is because the reactance of a capacitor is determined by its capacitance and the frequency of the applied voltage.

The reactance of a capacitor is inversely proportional to the frequency, which means that as the frequency increases, the reactance decreases. This is why at the resonant frequency, where the frequency is equal to 1/\sqrt{}LC, the reactance is at its minimum value of 1/\sqrt{}LC.

At other frequencies, the reactance can be calculated using the equation Xc = 1/(2(pi)fC), where f is the frequency and C is the capacitance. This equation shows that the reactance is directly proportional to the capacitance. This means that as the capacitance increases, the reactance also increases.

In summary, the reactance of a capacitor is not a fixed value, but it depends on the frequency and capacitance. At the resonant frequency, the reactance is 1/\sqrt{}LC, but at other frequencies, it can be different.