Phasor diagrams for RLC circuit and resonant frequency

[lys04]

Can someone check if my understanding is correct?

At resonant frequency, my understanding is that the magnitude of the reactances of the capacitor and the inductor have the same magnitude but they are 180 degrees out of phase, making the overall impedance of the circuit only consisting of the resistance from the resistor. In phasor diagrams, this means that the driving voltage and the current should be in phase. But the voltage across the capacitor and the inductor should still be 90 degrees apart from each other? Like separated by 90 degrees on the phase diagram (in general if the driving voltage has a phase).

Also in this diagram i'm not quite understanding the left and right images, can someone explain?

 

[LvW]

Assuming that you are speaking about a series resonant circuit (why didn`t you mention this?), Your diagrams look pretty good.

 

[tech99]

The diagrams look correct to me. The easy way to understand it for a series circuit is to notice that the same current flows in all three components, say 1 amp. Then the voltage across each component is just ZxI volts.
Relative to the current, inductor voltage leads, capacitor voltage lags and resistor voltage is in phase.
At resonance the inductor and capacitor voltages are equal magnitude - centre diagram. Below resonance the capacitor has greater reactance than the inductor, so has a higher voltage (left hand diagram). And conversely for the right hand diagram. The two reactive voltages subtract to give a resultant which is always at 90 degs to the voltage across the resistor.
If you come to study parallel RLC circuits, use the same method, but in this case all components have the same voltage and the currents differ. Assume 1 volt applied and then work out the current in each leg. The current in C will lead the voltage, that in L will lag and that in R wil be in p[hase with the applied voltage.

 

[sophiecentaur]

Also in this diagram i'm not quite understanding the left and right images, can someone explain?

The three diagrams show the voltage phasors for the three components as the frequency changes. At resonance, the volts across the L and C cancel out and the resulting Vs is the least possible magnitude (determined by the R). For a lower frequency, Vc will be higher than VL so there is a resultant which adds (vectorially) to the Vr and the overall resultant is the (leading) black arrow. For a higher frequency, the VL is higher and the resultant black arrow lags.
The lower the R value, the sharper the frequency response maximum.