How do I determine the resonance frequency of this circuit

Question

I have a circuit that consists of a voltage source in series with a resistor and a parallel of an inductor with a capacitor. I have to determine the resonance frequency of this circuit. I am very confused about this. First of all the impedance of the circuit is given by

$$Z=R+j(\frac{\omega L}{1-\omega^2 L C})$$

Now my thought was immediately to proceed as I did in the RLC series circuit i.e. to make the imaginary part of Z zero.

I obtain \$\omega=0\$. However the correct answer should be: $$\omega=\frac{1}{\sqrt{LC}}$$

But that would make the imaginary part of the impedance infinity and therefore the whole impedance infinity and the current zero. But isn't impedance when the current reaches its peak?

I'm so confused about all of this. I read that there is series impedance and parallel resonance but what should I peak and why are there 2 types of resonance. Shouldn't they be equivalent? Isn't resonance just the circuit behaving as a resistor?

Can someone explain me what is going on? Thanks!

Answer 1

Regarding series versus parallel resonance: only when a complete path exists, for the circulating currents, can resonance occur. In parallel resonance, the L and C are obviously in a tight loop. In series resonance, in some oscillators, the "circulating currents" take a path that included the VDD wiring, and the oscillator will fail **unless* a low-loss capacitor is used in VDD bypassing.

Answer 2

But isn't impedance when the current reaches its peak?

I'm assuming you mean resonance. That statement is true only for series RLC circuits, but is not the case in general.

Resonance frequency (in this case) is when the impedance of the inductor \$L\$ and capacitor \$C\$ are equal to each other. That should be your starting point. The rest of your assumptions are only true for RLC series and cannot be extended to parallel RLC.