Current phase between inductor and capacitor in LCR-circuit

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At resonance in an LCR circuit, the phase angle is zero, indicating that voltage and current are in phase. However, the current and voltage across the inductor and capacitor are out of phase by π/2, leading to energy oscillating between them. This phase difference results in the current being in quadrature with the voltage, which is crucial for understanding energy transfer in the circuit. The relationship between current and voltage in an ideal inductor and capacitor demonstrates that while the overall circuit voltage sums to zero at resonance, individual components do not share the same phase. The confusion arises from the treatment of energy calculations, where the phase relationship must be carefully considered.
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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?
 
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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.
 
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.
 
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.)
 
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