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?
Best Answer
It's not clear whether they are in series or parallel, because the first paragraph says they are series and the second paragraphs says they are in parallel. If they are in series, add the reactances to get the impedance. If they are in parallel, take the reciprocal of the sum of the reciprocals (i.e., the sum of the susceptances). Either way, you will get an impedance that is either 90 or -90 degrees.