Reactance Equal: Can Low Value Capacitor Replace High Value Inductor?

[The_Thinker]

Now if we take the impedence for a circuit. Xc for the capacitive component and Xl for the inductive component and equate them, that is we equate the impedance then we can get the same impedance from both a capacitive as well as a inductive load, we get something like this.


Now, in mathematical form,

Xc = Xl

1/2(pi)fc = 2(pi)fl

so we can equate the capacitance and inductive impedances for a specific frequency.

Now my question is using this, can we state that a low value capacitor can be used instead of a high value inductor from this? since the impedence is the same?

I have heard that it is not possible, so I am just a bit confused, what exactly impedence.

I understand that a capacitor has lagging current and an inductor has leading current and all that and I understand that therefore they are not that simple to be interchanged.

But If the Independence are equal, then they must have the same effect on the circuit right? So, can't they be interchanged? That is my question.. Although I am a bit confused...

 

[Manchot]

You are mistaken: you cannot make the reactance of a capacitor the same as an inductor. The impedance of a capacitor is 1/(j*2 pi f * C), which means that its reactance is -1 / (2 pi f * C). A capacitor and an inductor will always have opposite signs.