It all depends on the values of the components:If
the system will very slowly decay until the energy of the system reaches 0.
the system undergoes something which will look like a part of a oscillation and loses its energy very quickly
it oscillates with decreasing amplitude until its energy reaches 0.
In our case:
so the the system undergoes something which will look like a part of a oscillation and loses its energy very quickly
In order to find the equation of current of this RLC circuit we must be introduced to 2 things:
Neper angular frequency -> a feature of damped systems
In the case of parallel RLC circuit:
The equation of voltage of this critically damped system is:
After the switch is closed:
and due to C1:
so the current through C1 is:
By substituting the values VC1(0+),iIC1(0+) and a we get:
This is the equation of the voltage of the top common node of C1,L1,R1 after the switch is closed.