Need help simplifying equation to find the laplace transform of it

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SUMMARY

The discussion focuses on simplifying two differential equations from an electrical circuit to find the Laplace transform, specifically to analyze the step response using MATLAB. The equations involve two loops with variables I1 and I2, resistances R1 and R2, and a capacitor. The user seeks confirmation on the setup of the equations and is advised to differentiate them to eliminate integrals before applying the Laplace transform. The goal is to derive an equation that relates the output voltage across resistor R2 to the input voltage.

PREREQUISITES
  • Understanding of electrical circuit analysis, specifically loop analysis.
  • Familiarity with differential equations and their applications in circuit theory.
  • Knowledge of Laplace transforms and their use in solving differential equations.
  • Proficiency in MATLAB for simulating and analyzing circuit responses.
NEXT STEPS
  • Learn how to apply the Laplace transform to differential equations in electrical circuits.
  • Study MATLAB functions for simulating step responses of dynamic systems.
  • Explore techniques for simplifying complex equations in circuit analysis.
  • Investigate methods for deriving output voltage equations in RLC circuits.
USEFUL FOR

Electrical engineers, circuit designers, and students studying control systems or circuit analysis who need to simplify equations for Laplace transforms and analyze system responses using MATLAB.

formulajoe
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there are two loops in an electrical circuit. I've got two equations and two unknowns.
here are the equations

v(t) = I1*R1 + 1/c*int(I1*dt) - 1/c*int(I2*dt) - first loop
0 = LdI2/dt + R2*I2 - 1/c*int(I1*dt) + 1/c*int(I2*dt) - second loop

the capacitor is in the branch between the two loops.

Im drawing a blank on this. I need to simplify into one equation so I can find the laplace transform of the one equation.
the goal is to find the step response of the system using matlab.
 
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You'll want to differentiate both equations first, to get rid of those god awful integrals.

I need to simplify into one equation so I can find the laplace transform of the one equation.

There's nothing wrong with taking the Laplace transform first and then simplifying.
 
can i get a confirmation that i set up those differential equations properly? I am having some trouble with this still. if i differentiate, than i get derivative of the input. I am trying to find the output voltage which is across the R2 resistor.
 
im still having trouble with this problem. I've tried multiple methods including differentiation and solving for a variable and plugging it into the first equation but I am still where i started the other day. I am trying to find an equation that relates the output voltage across R2 to the input. I am confident my beginning equations are correct, but i don't know where to go from there.
 

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