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# Parallel RLC circuit

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How to find the equation of voltage of the top common node of R1,L1 and C1 after the switch is moved?

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Do you mean C2? (2 comments)
A circuit doesn't have a voltage (1 comment)

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It all depends on the values of the components:If

the system will very slowly decay until the energy of the system reaches 0.

If

the system undergoes something which will look like a part of a oscillation and loses its energy very quickly

If

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:

where:

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.

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