Figuring Out a General Solution for RLC Series Circuit

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SUMMARY

The discussion focuses on deriving a general solution for the differential equation dI/dt in an RLC series circuit. A participant seeks assistance in identifying errors in their calculations, specifically regarding the application of the quadratic formula. It was pointed out that the coefficient R was not squared under the radical, which is a critical mistake in solving the equation accurately. This oversight affects the resulting waveform, leading to incorrect outputs.

PREREQUISITES
  • Understanding of RLC circuit theory
  • Familiarity with differential equations
  • Knowledge of the quadratic formula
  • Basic circuit analysis skills
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  • Review the application of the quadratic formula in electrical engineering contexts
  • Study the behavior of RLC circuits under different conditions
  • Learn about the Laplace transform for solving differential equations in circuits
  • Explore simulation tools for visualizing RLC circuit waveforms
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Electrical engineers, students studying circuit theory, and anyone involved in analyzing RLC circuits and their transient responses.

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So, I have been trying to come up with a general solution for dI/dt in an RLC circuit.

I have attached the work I have done so far. I don't know where but I am making a mistake and the waveform is not coming out right. Would really appreciate a look over my work to see if I made any obvious errors.
 

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You did not use the quadratic formula properly. You forgot to square the coefficient R under the radical.
 

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