# Resonant frequency in parallel

I'm currently learning about resonant frequency and harmonics under ac theory in tafe, and I've read a few things about resonant frequency in parallel, and it seems as if impedance at resonant frequency is at maximum, but when calculating impedance with Pythagoras theorem, we say that Xl and Xc cancel each other out. Therefore impedance is equal to resistance, or at minimum. I understand that there is current flow from the inductor to capacitor, but I'm having trouble because it seems like the two cancel each other out, can anyone help me understand a bit more of a what's going on? Thanks

XL and XC cancel each other in a series resonant circuit but in parallel resonance they produce an infinite impedance.

XL is jwL and

XC is 1/jwC

In parallel they form this impedance: -

Z = $\dfrac{j\omega L \cdot \frac{1}{j\omega C}}{j\omega L +\frac{1}{j\omega C}}$

Z = $\dfrac{j\omega L}{1-\omega^2LC}$

When $\omega^2 LC =1$, the denominator is zero therefore the impedance is infinite.

• Where j indicates a 90 degrees phase shift and w is angular frequency? But that makes sense :) thank you! Jul 3 '14 at 8:35
• @DanielSmith correct Jul 3 '14 at 8:44