I have a generic LC circuit where the inductor and capacitor are in series and we have alternating EMF. I'm trying to find the the impedance of the circuit with phasors.
A phasor diagram shows inductive reactance $\frac{\pi}{2}$ anticlockwise from the EMF phasor (taken as reference with it pointing along "+x axis") and capacitive reactance $\frac{\pi}{2}$ clockwise from EMF phasor. I subtract the 2 reactances since they are parallel (**I mean the phasors are anti-parallel in the phasor diagram) and so I believe that whichever reactance is more dominant, the phase difference the impedance makes with the EMF phasor is the same as that for the more dominant reactance, i.e. either $+\frac{\pi}{2}$ or $-\frac{\pi}{2}$. But I came to find out that it is actually:$$\theta=\tan^{-1}(|\omega l-\frac{1}{\omega C}|)$$
I cannot reason why. Why is the phase difference as such?