How Do You Calculate Initial Conditions in First Order Transient Circuits?

[Crutchlow13]

Homework Statement

It asks me to find io(t=0^-), io(t=0⁺), and Vc(t=0^-). C=100μF R= 2kΩ

Homework Equations

V=I*R, i(t)= i(∞)+[i(0⁺)-i(∞)]*e^-t/τ, Vc(0-)=Vc(0+)

The Attempt at a Solution

[/B]I first tried to calculate Vc(0-) as it will be the same as Vc(0+), stating that at t=0^- the capacitor acts as an open circuit because it's been fully charged (the switch has been off since -∞), and I think it's 24V but I'm not sure about that. I also calculated io(0-), which is 2A, but I couldn't go any further.

Thank you guys.

 

[gneill]

Can you show some details of your calculations for initial values of V_c and i_o?

To me, 24 V looks too low and 2 A looks to large...

 

[Crutchlow13]

You're right about the io, I believe it should be 36-12=io(2000+3*2000+2*2000) io=2x10^-3 A. For the Vc I just did 36-12, but now that I think of it maybe it's 32, as the voltage drops 4V in the first resistance. I struggle a lot to calculate voltages when the capacitor is in the middle of the circuit.

 

[gneill]

You're right about the io, I believe it should be 36-12=io(2000+3*2000+2*2000) io=2x10^-3 A. For the Vc I just did 36-12, but now that I think of it maybe it's 32, as the voltage drops 4V in the first resistance.

Those are better values You should always lay out the equations, particularly to confirm any "intuitive" results.

 

[Crutchlow13]

Those are better values You should always lay out the equations, particularly to confirm any "intuitive" results.

Yeah you're right, thanks. I'm now trying to calculate io(0⁺) and io(∞). For io(0+) I replaced the capacitor for a voltage source of 32V (assuming the other calculations were right) and applying KVL I figured that the intensity should be 32/6000= 5,3x10^-3. But I'm not sure how the capacitor acts when t=∞ /:

 

[gneill]

At steady state, capacitor currents go to zero. Effectively they "look like" an open circuit to the rest of the circuit. So for t=∞ remove the capacitor and find the potential across the points where it was connected.

 

[Crutchlow13]

At steady state, capacitor currents go to zero. Effectively they "look like" an open circuit to the rest of the circuit. So for t=∞ remove the capacitor and find the potential across the points where it was connected.

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Thank you very much @gneill, my teacher posted the solution and it turns out the second calculations I assumed (with your help) were right! :D Do you know any good books with this type of exercices so I can practice for my exam? Thank you again for your time.

 

[gneill]

Thank you very much @gneill, my teacher posted the solution and it turns out the second calculations I assumed (with your help) were right! :D Do you know any good books with this type of exercices so I can practice for my exam? Thank you again for your time.

Well done.

I don't know of any particular books, but a Google search on "first order circuits examples" will turn up lots of hits.