Electric Impedance: Exploring ω2LC=1

[whatisreality]

Homework Statement

Consider a circuit with a capacitor C in series an inductor of inductance L. Explain what happens when ω²LC=1, without calculations, using your knowledge and intuition.

Homework Equations

1/Z = 1/impedance = 1/(iωL) +1/(iωC)
i is pure imaginary.

The Attempt at a Solution

Well, unfortunately I have no intuition. I don't know what the quantity ω²LC represents, but it appears in the equation when you rearrange to find Z. So when I worked out Z, it was -1/(iωC+iωL) when the set condition is met. Which is a bit weird, because -ve resistance makes no sense...?
I've obviously gone wrong somewhere!

 

[BvU]

Yes, a capacitor has impedance $$1\over j\omega C$$
Look here for some ideas

 

[whatisreality]

So when ω²LC=1 then the inductive and capacitive reactances are equal. The current is oscillating at the resonant frequency of the circuit?

 

[BvU]

That's right. Nothing wrong with your intuition.
Reactances are equal and opposite. So together they are 'zero'. $\bf V = Z I$ (bold face to mark them as complex): there can be huge currents shooting back and forth with 'no' voltage needed to whip them up. In reality you can't have a lossless system, so characteristics of an RLC circuit sneak in.