Fraction Simplification: Solving Equations with Constants C, L, and R

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SUMMARY

The discussion focuses on simplifying equations involving constants C, L, and R in the context of control systems. The user is attempting to manipulate the equations to achieve a cleaner form, specifically aiming for the expression V1(s) = V2(s)(1+sCR). The provided equations include i(s) and V2(s) in terms of these constants, but the user struggles with achieving the desired simplification. The conversation emphasizes the importance of substitution and algebraic manipulation in deriving the correct forms.

PREREQUISITES
  • Understanding of Laplace transforms and their applications in control systems.
  • Familiarity with algebraic manipulation of equations involving constants.
  • Knowledge of transfer functions and their representation in the s-domain.
  • Basic concepts of circuit analysis, particularly in relation to RLC circuits.
NEXT STEPS
  • Study the process of Laplace transform simplification for control systems.
  • Learn about transfer function derivation and manipulation techniques.
  • Explore the use of symbolic computation tools like MATLAB or Mathematica for equation simplification.
  • Investigate the implications of RLC circuit parameters on system behavior and stability.
USEFUL FOR

Control system engineers, electrical engineers, and students studying circuit analysis who are looking to improve their skills in algebraic manipulation of equations involving constants in the s-domain.

jkface
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I have the following two equations

5bCv09x.png

3Eq3tTM.png


C, L, and R are all constants.

I need to somehow get the above two equations and get it to look like this:

ieBherg.png


But I can't get mine to look that nice. I have V1(s) = V2(s)(1+sCR) and I substituded it into equation 1 and it ends up looking messy. Any help would be appreciated.
 
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Show us your work and you may get some helpful suggestions.
 
i(s) = V2(s)(1+sCR) / sL + (V2(s)(1+sCR) - V2(s)) / R
i(s) = V2(s)( (1+sCR) / sL + sCR / R)
V2(s) = i(s) (sL / (1+sCR) + 1 / sC) = i(s) ((s^2 * LC + 1 + sCR) / sC(1+sCR))
V2(s) = i(s) ((s^2 * LC + 1 + sCR) / (sC+s^2 * C^2 * R))

this is obviously not what I'm supposed to have.
 

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