# Weird Transient Circuit with Two Capacitors...

Discussion in 'Homework Help' started by blah2222, Dec 10, 2010.

1. ### blah2222 Thread Starter Well-Known Member

May 3, 2010
554
33
Hi, so after doing all of these transient circuits (RL, RC, and RLC), I wondered how a circuit with two capacitors would function, so I made up this circuit and thought that it would be an easy solve... I pretty much got it to the point where I have two differential equations but have no clue how to solve for their voltages...

$t = 0^-:$

$V_{c1} = 4 V$
$V_{c2} = 0 V$

$t >= 0^+:$

$\frac{C_{1}dVc_{1}}{dt^2} = \frac{4 - 4V_{c1} + V_{c2}}{2}$

and

$\frac{C_{2}dVc_{1}}{dt^2} = \frac{V_{c1} - V_{c2}}{2}$

Here's the circuit that I am referring to:

Any help would be wonderful, thanks!
JP

Last edited: Dec 10, 2010

Feb 5, 2010
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May 3, 2010
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4. ### thatoneguy AAC Fanatic!

Feb 19, 2009
6,357
718
Have you installed LTSpice and run the .tran analysis of your circuit above?

It can be done by working through the calc, for that problem, which isn't a type of circuit that comes up in a standalone application.

This is the reason EDA software has replaced slide rules and even HP Calculators in circuit design, that and the staggering amount of "more" one can do with "less" compared to the vacuum tube days.

--ETA: It may seem like "cheating", but you will often see something in the output that will make a lightbulb go on. Once you fully understand why what happens (visual feedback helps a lot), writing/solving the equations isn't such an algebraic/calculus ridden nightmare.

5. ### pawan.waikato New Member

Feb 23, 2013
1
0
Hi JP,

Did you manage to solve the equation? I am pondering on same problem....
I will really appreciate if you could let me know if you manage to solve this 2 capacitor transient problem...

Cheers,
Pawan

6. ### blah2222 Thread Starter Well-Known Member

May 3, 2010
554
33
Hi, yeah I just simulated it in LTSpice and then verified the solution by solving for Vc1 and Vc2 in the time domain and then using the Laplace Transform to make the math a bit cleaner. Still a lot of work though.

See attached.

Cheers,
JP

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