Impedance of Capacitive Reactance

It was learned in the chapter "Capacitor" that for the pure capacitor of [Fig. 1], the current leads the voltage by $90^\circ$ and that the reactance of the capacitor $X_C$ is determined by $1/wC$. Applying Ohm's law and using phasor algebra, we find Since i leads v by $90^\circ$, i must have an angle of $+90^\circ$ associated with it.
To satisfy this condition, $\theta_C$ must equal $-90^\circ$. Substituting $\theta_C=-90^\circ$, we obtain so that in the time domain, The fact that $\theta_C=-90^\circ$ will now be employed in the following polar format for capacitive reactance to ensure the proper phase relationship between the voltage and current of an capacitor. The boldface roman quantity $Z_C$, having both magnitude and an associated angle, is referred to as the impedance of an capacitive element. It is measured in ohms and is a measure of how much the capacitive element will "control or impede" the level of current through the network (always keep in mind that capacitive elements are storage devices and do not dissipate like resistors). The above format, like that defined for the resistive element, will prove to be a useful "tool" in the analysis of ac networks. Again, be aware that $Z_C$ is not a phasor quantity, for the same reasons indicated for a resistive element.