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:
it will very slowly decay without any oscillation.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 the series RLC circuit it is:
The natural angular frequency -> the frequency response of the system under no damping
In a RLC circuit it is equal to:
The equation of current of this overdamped system takes this form:
Now lets go calculate s1 and s2:
After the switch is closed:
and due to L1:
so the voltage between L1 is:
By substituting the values of s1,s2 VL1(0+),L1 and IL1(0+) to (1) and solving the system we get:
This is the equation of the current of the loop consisting of C1,L1,R1 after the switch is closed.