# reactance of a capacitor & inductor

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#### dinesh401

The reactance of a capacitor is indicated sometimes as Xc=1/j2pifc and sometimes as Xc=1/2pifc.
So what is the reason for this, which notation we have to follow during calculations.
and what is the difference between these two....?

The complex "j" operator implies that there is a phase-shift associated with the component (i.e., current and voltage in the device are out of phase). If you are just trying to calculate the resistive part of the complex impedance, you don't need the "j".

"as Xc=1/j2pifc and sometimes as Xc=1/2pifc." I have never seen it written this way before (even if its numerically correct) its written as :- -j 1/2PIfc, likewise the reactance of an inductor is +j 2PIfl. this is so during a calculation the + and - js can be subtracted or added leaving a single answer of + J.... or -j....
Frank

I have never seen it written this way before (even if its numerically correct) its written as :- -j 1/2PIfc,

Surprisingly - I have seen it written this way very often:

Xc=1/sC with s=jw=j*2Pi*f we get:

Xc=1/(jwC)=1/(j*2Pi*f*C).

Of course, now you can insert the identity j=-1/j .

The debatable point is wheter the formula sign Xc designates the imaginary impedance or a scalar value (measured in ohm).

At least some text books are using it in the latter meaning, e.g.

Code:
Z = R + jXL - jXc

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