Differential Equations RLC Circuits

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SUMMARY

The discussion centers on solving a series RLC circuit with an electromotive force described by E=200e^(-100t) V, a resistor of 80 ohms, an inductor of 0.2 H, and a capacitor of 5x10^-6 F. The initial conditions specify that both the current and charge on the capacitor are zero. Participants emphasize the importance of recognizing that the same current I(t) flows through all components and suggest using Kirchhoff's laws to relate the voltages across the resistor, inductor, and capacitor.

PREREQUISITES
  • Understanding of RLC circuit components (resistor, inductor, capacitor)
  • Familiarity with Kirchhoff's voltage law
  • Knowledge of differential equations
  • Basic principles of electromotive force (EMF)
NEXT STEPS
  • Study the application of Kirchhoff's laws in RLC circuits
  • Learn how to derive differential equations for series RLC circuits
  • Explore the concept of transient response in RLC circuits
  • Investigate the use of Laplace transforms for solving circuit equations
USEFUL FOR

Electrical engineering students, circuit designers, and anyone involved in analyzing RLC circuits and their transient behaviors.

kings13
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Homework Statement



A series RLC circuit has an electromotive force given by E=200e^(-100t) V, a resistor of 80 ohms, an inductor of 0.2 H, and capacitor of 5x10^-6 F. If the initial current and charge on the capacitor are zero, find the current at any time t>0.


Homework Equations



??

The Attempt at a Solution



i am not begging for someone to solve the whole problem for me, just to get it started
 
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OK, start by observing that the same current is flowing through all three components (R, L and C) at any time t because they are in series. Call this current I(t).

Let the voltage drop across each of the components be represented by V_R(t), V_L(t) and V_C(t).

Can you now list some equations relating I(t) to each of those voltages?

What can you say about the sum of those three voltages (Kirchoff's laws)?
 

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