Solving RC Circuits with Switch: Finding Vs(t) and Vc(t)

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SUMMARY

The discussion focuses on solving RC circuits with a switch to determine the voltage across the source, Vs(t), and the capacitor, Vc(t). The user attempts to analyze the circuit by considering two scenarios: the switch being ON and OFF. To proceed, it is essential to apply Kirchhoff's Current Law (KCL) at the node above the capacitor and formulate the corresponding differential equation, incorporating initial conditions from the open switch state at t=0.

PREREQUISITES
  • Understanding of RC circuit theory
  • Familiarity with Kirchhoff's Current Law (KCL)
  • Ability to solve differential equations
  • Knowledge of initial conditions in circuit analysis
NEXT STEPS
  • Learn how to apply Kirchhoff's Current Law (KCL) in circuit analysis
  • Study differential equations related to RC circuits
  • Explore initial condition applications in circuit problems
  • Review examples of voltage and current analysis in switched circuits
USEFUL FOR

Electrical engineering students, circuit designers, and anyone studying transient analysis in RC circuits will benefit from this discussion.

frutti
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Homework Statement


i need to find the Vs(t) and Vc(t)

http://img32.imageshack.us/img32/9071/circuiten.jpg

The Attempt at a Solution


since there is a switch i used two cases to find the Vc
one with switch on and switch off
switch on
http://img704.imageshack.us/img704/6180/switchon.jpg
and switch off
http://img265.imageshack.us/img265/3259/switchoff.jpg

but I am lost after this...
help me!
 
Last edited by a moderator:
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frutti said:

Homework Statement


i need to find the Vs(t) and Vc(t)

http://img32.imageshack.us/img32/9071/circuiten.jpg

The Attempt at a Solution


since there is a switch i used two cases to find the Vc
one with switch on and switch off
switch on
http://img704.imageshack.us/img704/6180/switchon.jpg
and switch off
http://img265.imageshack.us/img265/3259/switchoff.jpg

but I am lost after this...
help me!

The cap still needs to be there with the switch ON.

Write the KCL equation for the node at the top of capacitor (with the bottom of the cap being the common "ground" node), and solve the resulting differential equation, using the initial conditions from when the switch was open (assume the switch is closed at t=0). Show us your work, so we can help you more if you need it.
 
Last edited by a moderator:

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