Visualising current in the LCR circuit I just went through the theory of the serial LCR circuit.
There current and voltage are 90 degrees out of phase with each other. Now I was trying to imagine an animation with just dots. And I visualized it in my head like a longitudinal sound wave. So, having alternate zones where density of dots is squeezed and stretched.
But in a longitudinal sound wave pressure and the pass-through rate are in the phase.


*

*How would 90 deg phase difference between pressure & current look like in LCR circuit's AC if visualized as oscillating dots? 

*Will it be longitudinal wave?

 A: Perhaps this is what you are looking for:  
Screen capture:

http://www.falstad.com/circuit/
The default circuit, as shown, is an LRC circuit.  
On the Schematic:
Gray is 0V
Green is Positive Voltage
Red is Negative Voltage
The yellow dots are a visualization of current: positive holes.
The graphs along the bottom, from left to right, are for the Inductor, Capacitor, and Resistor.
The Green waveform is the voltage across the component.
The Yellow waveform is the current through the component.

So to answer your questions:  


*

*In the animation above, the 90 deg phase difference is shown since the yellow dots' velocity (current) is maximum when the voltage across the inductor is 0V (gray on both sides). The dots' velocity is 0 when there exists the maximum absolute voltage (red or green).

*Current shouldn't be represented as longitudinal waves, since the current through a series circuit must be all equal. (It could possibly be represented with longitudinal waves in the context of electron charge on a capacitor, but electrical engineers still represent this as current flow, called displacement current.)

