Find RLC Values in RLC Series Circuit

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Discussion Overview

The discussion revolves around determining the values of resistance (R), inductance (L), and capacitance (C) in an RLC series circuit based on a given current response after applying a unit step voltage. Participants explore the application of Laplace transformations and differential equations in this context.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents the current response as i(t)=(125/24) * exp(-700t)* Sin(2400t) mA and seeks to find R, L, and C values.
  • Another participant suggests writing the differential equation for the circuit and applying initial conditions, questioning whether the use of transforms is required.
  • A participant provides the Laplace transformation of the current as I(s)=12500/[(s+700)^2+2400^2] and applies Kirchhoff's Law, resulting in I(s)=1/[s*(LC*s^2+RC*s+1)], expressing confusion over the differing degrees of the denominators.
  • One participant argues that using the Laplace transformation is preferable to solving the differential equation due to the complexity involved.
  • Another participant challenges the correctness of the derived expression from Kirchhoff's Law, indicating a mismatch with the provided I(s) and expressing uncertainty about the next steps.

Areas of Agreement / Disagreement

Participants express differing opinions on the best approach to solve the problem, with some favoring Laplace transformations while others suggest differential equations. There is no consensus on the correctness of the derived expressions or the next steps to take.

Contextual Notes

Participants note discrepancies in the degrees of the denominators in the Laplace transformations, indicating potential misunderstandings or misapplications of circuit laws. The discussion remains focused on the mathematical relationships without resolving these issues.

danilorj
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Guys,
Let's suppose we have RLC series circuit feeded by tension source initially with no energy stored. When we apply an unitary step of tension at t=0 at the terminals of the circuit, we observe a current of i(t)=(125/24) * exp(-700t)* Sin(2400t) mA that goes around the circuit for t>0s.
I want to find the values of R, L, C.
I was trying to match the laplace transformation of the current above to the laplace transformation of the circuit for the current but no success.
 
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danilorj said:
Guys,
Let's suppose we have RLC series circuit feeded by tension source initially with no energy stored. When we apply an unitary step of tension at t=0 at the terminals of the circuit, we observe a current of i(t)=(125/24) * exp(-700t)* Sin(2400t) mA that goes around the circuit for t>0s.
I want to find the values of R, L, C.
I was trying to match the laplace transformation of the current above to the laplace transformation of the circuit for the current but no success.

Can you just write the differential equation for the current and voltage of the circuit, solve the DE and apply your initial conditions? That should get you the answer as well. Or are you required to use transforms?
 
Let me explain it better
The Laplace transformation of the given current is I(s)=12500/[(s+700)^2+2400^2]
And if I apply the Kirchhoff Law Tension around the RLC series circuit I get
I(s)=1/[s*(LC*s^2+RC*s+1)]. But I don't know what to do with this. They seem to be different, one has degree 3 and the other has degree 2 in the denominator.
 
And I think the best way of doing this is using the Laplace transformation, cause solving the differential equation would take a very hard work, and I don't think it's going to work as well.
 
danilorj said:
Let me explain it better
The Laplace transformation of the given current is I(s)=12500/[(s+700)^2+2400^2]
And if I apply the Kirchhoff Law Tension around the RLC series circuit I get
I(s)=1/[s*(LC*s^2+RC*s+1)].
Show us how you got this. I don't think it's correct, which is why it's not matching up with the I(s) you were given.
But I don't know what to do with this. They seem to be different, one has degree 3 and the other has degree 2 in the denominator.
 

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