I always thought that capacitors (when used in phasor analysis) just had an impedance of $$1/jwc$$.
I understand that impedance $$Z=R+jX$$where R is resistance and X is reactance. Now, in one book I found that the reactance of a capacitor is $$1/wc$$. So the impedance for the capacitor would be $$j/wc$$.
How come it's j/wc here and we always used 1/jwc before??
Some authors specify the reactance of basic circuit elements as an absolute value. Although this is confusing it is not so uncommon. The "trick" is to remember that if you define reactances as:
\[ X_L = \omega L \qquad X_C = \frac{1}{\omega C} \]
then the impedance for an inductor and a capacitor are:
\[
Z_L = j X_L = j \omega L
\qquad
Z_C = -j X_C = \frac{- j}{\omega C} = \frac {1}{j \omega C}
\]
The problem with this approach is that you must always remember that the reactance as the imaginary part of a generic impedance (i.e. X = Im(z)) is not the same reactance you speak of when talking about "pure" capacitors (there the sign of the reactance is embedded in the value of X).
