Help with Circuits Capacitance & Inductance

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Discussion Overview

The discussion revolves around solving circuit problems involving capacitance and inductance, specifically focusing on node analysis, Thevenin's theorem, and the use of operational amplifiers (opamps). Participants seek assistance with equations and initial conditions related to circuit analysis.

Discussion Character

  • Technical explanation
  • Homework-related
  • Debate/contested

Main Points Raised

  • One participant questions the labeling of current in a diagram, suggesting it should be I(t) instead of IL(t).
  • Another participant requests clarification on how to find the Thevenin equivalent resistance (R) and discusses their approach to determining initial and final conditions for an inductor.
  • There is a discussion about the use of node analysis for finding output voltage (Vo) and the need to replace Vp with Vs in the equations.
  • Some participants propose that Vp should be treated as equal to Vn in ideal opamp scenarios, while others suggest maintaining the distinction for clarity in non-ideal cases.
  • A later reply provides a method for solving simultaneous differential equations in the Laplace domain, offering a specific approach to the circuit problem.

Areas of Agreement / Disagreement

Participants express differing views on the treatment of Vp and Vn in the context of opamps, with some advocating for maintaining the distinction while others assert they are equal in ideal conditions. The discussion remains unresolved regarding the best approach to the circuit problems presented.

Contextual Notes

Participants' approaches depend on their assumptions about ideal versus non-ideal opamps and the initial conditions for the circuit elements, which are not fully clarified. There are also unresolved mathematical steps in the proposed solutions.

deyiengs
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The images tell it all. Please help someone.


http://image.cramster.com/answer-board/image/200941884006337564080009162509346.jpg


on this diagram, the expression IL(t) should read I(t).

http://image.cramster.com/answer-board/image/2009418845296337564112974787505740.jpg
 
Last edited by a moderator:
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Welcome to PF!

Hi deyiengs! Welcome to PF! :wink:

Show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
 
Thanks Tiny-tim for taking your time. I planned to post what i had but i forgot.
On the first one, how do you get R- thevinin? If that's the way to go about it?.
On the second one I need the initial and final conditions. I used -5mA and did a source transformation to get -2.1mA as the initial consition. I used 5mA for final and got 2.1mA as the final conditio for the inductor. Then used the formula:
iL = (i(initial) - i(final))e^(-1/tc)+ i(final)
My tc was 3.3333us
Then used VL = L di/dt

Is that close to the correct way or did I deviate
 
On the following diagram, I have the following for finding Vo:

node analysis on the top nope of the Vn
http://image.cramster.com/answer-board/image/cramster-equation-2009419162557633757551572010000561.gif
This would lead to
http://image.cramster.com/answer-board/image/cramster-equation-20094191627356337575525582600002527.gif

but i need to replace Vp by Vs.

Hence for the node on the bottom part I have:
http://image.cramster.com/answer-board/image/cramster-equation-200941916329633757555299510000920.gif
I'm stuck here how can I factor out Vp on the above equation. is it possible if it it how.

http://image.cramster.com/answer-board/image/2009419162211633757549313416250747.jpg

If not is there another way of solving this equation.
 
Last edited by a moderator:
In the first two equations of the opamp problem, shouldn't the Vp be Vn instead?
 
The Electrician said:
In the first two equations of the opamp problem, shouldn't the Vp be Vn instead?

yes but Vp = Vn
 
Someday you may have to find a transfer function where the opamp isn't ideal. In that case, Vp#Vn, so it's good practice to use the symbol for the actual node that you're writing an equation for. Then at the end, if the opamp is ideal, substitute Vp=Vn. This way, you avoid mistakes in setting up your equations.
 
The Electrician, could you help me solve it if you can please
 
You can either solve your two simultaneous differential equations, or you can solve it in the Laplace domain. I would do the latter. Have you studied the use of the s-variable for solving AC circuits?

Set up two equations:

s*C*Vn + (1/R)*(Vn-Vs) = 0

s*C*(Vp-Vs) + Vp/R = 0

Now, you also know that Vp = R/(R + 1/(s*C)) * Vs by the voltage divider rule, and Vp=Vn.

Substitute that that last equation, Vp = R/(R + 1/(s*C))*Vs, for both Vp and Vn in the first two equations. Then you will have two simultaneous equations you can solve with simple algebra.

The solution is Vo = s*R*C*Vs, which in the time domain is Vo = R C d/dt(Vs). This ignores initial values for charge on C.
 

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