Can the RLC Circuit Homework be Solved Using Different Methods?

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Discussion Overview

The discussion revolves around solving an RLC circuit homework problem using different methods. Participants explore the validity of using a differential equation approach versus a current summation approach to find the inductor current, iL, given specific circuit parameters and initial conditions.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant presents the initial conditions and equations for the RLC circuit, providing a solution for v(t) and expressing a desire to find iL using a different method.
  • Another participant suggests that using the equation v(t) = L*di/dt should work if v(t) is correct and requests to see the working steps.
  • A third participant asks for clarification by requesting to see the work done to solve for iL.
  • The original poster shares their integration attempt for iL, noting that while the form of the answer was correct, the coefficients did not match those obtained from the other method.

Areas of Agreement / Disagreement

The discussion remains unresolved, with participants exploring different methods without reaching a consensus on the validity of the approaches or the correctness of the results.

Contextual Notes

There are indications of potential errors in the coefficients obtained from the integration, but the specific reasons for these discrepancies are not discussed. The validity of using the differential equation approach in this context is also questioned without a definitive resolution.

TheBlueDot
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Homework Statement


Capture.PNG


R = 125 ohms, L = 200 mH, C = 5 uF, initial current in L is -0.3A, and initial voltage across C is 25V.

Homework Equations


v(t) = (Bcos(wt)+Csin(wt))e^(-at)

The Attempt at a Solution


I've solved for v(t) t>0 and got 25e^(-800t)(cos(600t)+ (4/3)sin(600t)). The second part is to solve for iL for t>0. In class, we've been solved for iL using iL+iR+iC = 0 →iL = -iR-iC but I want to solve for iL using v(t) = L*di/dt and I can't get the same answer as the other method. Is this not valid for this case? Thanks!
 
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TheBlueDot said:
I want to solve for iL using v(t) = L*di/dt
It should work, providing you have v(t) correct. So you're going to integrate v(t). Can you attach your working?
 
Can you show your work?
 
Thanks for the responses.
I had iL = (1/L)∫[25exp(-800t)*[cos(600t)+(4/3)sin(600t)] ]dt and I used WolframAlpha to evaluate the integral. The answer was in the right form but the coefficients were off. Thanks!
 
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