# Current phase between inductor and capacitor in LCR-circuit

1. Jul 16, 2013

### Order

At resonance ($\omega_0^2= 1/LC$) in an LCR-Circuit the phase angle given by
$$\theta=\tan^{-1}\left( \frac{\omega L - 1/\omega C}{R} \right)$$
obviously is zero. And still there are other phases to deal with. This I don't understand. Let me elaborate.

For example when calculating the amount of stored energy at resonance, then you can visualize that the energy goes back and forth between capacitor and inductor. So they are not in phase, but are in fact out of phase by $\pi /2$, or rather the current is.

Now my question is: In what equation (or diagram) is this clearly marked?

2. Jul 16, 2013

### wotanub

This shows the problem with perfect resonance. You know the phase angle is π/2, so plug that into the equation you used, and you'll find that must mean the parameter of the arctan function is some really huge or really small number (let's say... infinity).

Notice the parameter goes to infinity as R goes to 0. But R can't be zero in a real circuit.

3. Jul 17, 2013

### Baluncore

At resonance the CURRENT flowing is in quadrature with the VOLTAGE.

For the inductor; v = L * di/dt
If di/dt is a sine wave then v must be a cosine. Hence the quadrature.

4. Jul 17, 2013

### Order

Ok, let's see if I got things right:

1. The current is (for an ideal inductor with no capacitance) equal throughout the LCR-Circuit. (This is so because of Kirchoffs first rule.)

2. The voltage is not in phase between the different parts of the Circuit but at resonance it all adds up to zero.

3. The energy in the inductor is dependent of the current, whereas the energy of the capacitor is dependent of the voltage. And when the voltage is $\pi /2$ out of phase to the current (especially in the capacitor), the effect is that energy goes back and forth between inductor and capacitor. (In the book I read they put the current out of phase, when calculating the energy, which confused me.)