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Parent

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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2 comment threads

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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1 comment thread

Why are you answering your own questions? If you already know the answers why even post the question ... (6 comments)

Comments on Parallel RLC circuit

Why are you answering your own questions? If you already know the answers why even post the question ...
Carl‭ wrote about 1 month ago:

Why are you answering your own questions? If you already know the answers why even post the question in the first place?

MissMulan‭ wrote about 1 month ago:

Because it is useful if someone wants to ask something relevant to the question.

Olin Lathrop‭ wrote about 1 month ago:

@Carl: Self-answered questions are allowed here. Of course a self-answered question should be the kind that someone else might reasonably run into, and both the question and answer must be well written, well presented, and correct.

Carl‭ wrote about 1 month ago:

Olin Lathrop‭: Understood. But this doesn't seem like a question that matches the description you have given, in my opinion.

MissMulan‭ wrote about 1 month ago:

@Carl please clarify?Isnt it well written,correct or well presented?

Carl‭ wrote about 1 month ago:

MissMulan‭ The question and answers you have given are poorly presented and not easy to read/understand. The question is too specific to be useful for anyone other than yourself. And most importantly, the solution in your answer is incorrect! That is unacceptable and, honestly, embarassing.

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