In AC, there are $R$, $C$, & $L$ or $R$, $X_C$, & $X_L$. $$ X_C = \frac{1}{\omega C} $$ where $\omega=2\pi f$.
But sometime we're using the $X_C = \frac{1}{j\omega C}$. I understand the $j$ is the imaginary unit and it's current lead voltage in capacitance circuit. But why does the equation sometimes have $j$ and sometimes don't?
But why does the equation sometimes have j and sometimes don't?
The reactance $X$ is the imaginary part of the impedance $Z$ (which is a complex number):
$$Z = R + jX$$
and so, $X$ is a real number, i.e., there should never be an $i$ or a $j$ in the formula for a reactance.
Thus
$$X_L = \omega L,\qquad Z_L = jX_L = j\omega L$$
$$X_C = -\frac{1}{\omega C}, \qquad Z_C = jX_C = -j \frac{1}{\omega C} = \frac{1}{j\omega C}$$
