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Second order circuit with 2 capacitors to differential equation 
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#1
Jan2612, 06:44 AM

P: 2

hello i need help with this,
what is the differential equation for the voltage v2 (t). sorry for my english 


#2
Jan2612, 06:49 AM

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P: 26,148

hello nicksname! welcome to pf!
show us what you've tried, and where you're stuck, and then we'll know how to help! 


#3
Jan2612, 07:11 AM

P: 2

i know how it works with inductors. to find differential equation v with KVL (Kirchhoff's current law). but I've never done it before for the capacitor to v2(t). writing. i know I need to use Kirchhoff's voltage law. but that it is.



#4
May712, 09:41 AM

P: 39

Second order circuit with 2 capacitors to differential equation
Gah I need help with a similar problem and it's frustrating that it's not solved yet. I know how to substitute when there's an inductor and a capacitor, but it beats me how to do it when the energy savers are both the same circuit element.
So far I've got 2 helpful mesh equations (my problem has 3, but i used the last one to define the currents in terms of voltage derivatives) and I've replaced all the currents by Cdu/dt, but I don't know what to do next to get rid of the du/dt for the first capacitor. It looks like I could cancel out the Uc1s by substituting the equations into each other, but I need some other equation that I can't think of yet for the first du/dt I mentioned. 


#5
May712, 11:32 AM

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You may have two different currents in the two lower wires so you should set up two first order differential equations describing those. If you are required to have a single equation, you can combine those into a single second order equation for for either one of the currents.



#6
May712, 12:03 PM

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#7
May712, 12:25 PM

P: 39

I think I figured it out. When I did it (my problem has an extra loop, so you might have to do something slightly different), after I substituted everything I could I ended up with two mesh equations both in terms of V1, V2, dV2/dt, and one had dV1/dt, and then got stuck for a while. But then I figured out that you could solve the equation that did not have dV1/dt in it for V1, then I derived it to get another equation which put dV1/dt in terms of only V2 and dV2/dt. That gave me enough equations to solve the rest of the problem using only algebra.
Was this helpful? I can try solving the entire problem for you if you want. 


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