Help with Circuits Capacitance & Inductance

[deyiengs]

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

 

[tiny-tim]

Welcome to PF!

Hi deyiengs! Welcome to PF!

Show us what you've tried, and where you're stuck, and then we'll know how to help!

 

[deyiengs]

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

 

[deyiengs]

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.

 

[The Electrician]

In the first two equations of the opamp problem, shouldn't the Vp be Vn instead?

 

[deyiengs]

In the first two equations of the opamp problem, shouldn't the Vp be Vn instead?

yes but Vp = Vn

 

[The Electrician]

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.

 

[deyiengs]

The Electrician, could you help me solve it if you can please

 

[The Electrician]

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.