RCC circuit, posible mistake with constants

[1f5]

Homework Statement

There's a circuit, with a capacitor C1, Resistor R1, and another capacitor C2.
In t=0 ; C1 is charged with 2 V and C2 with 1 V
The value of resistor is 1 ohm, C1= 1 F C2=0.5 F

Homework Equations

Kirchoff voltage law.
Capacitor voltage at any given time. (integral form)

The Attempt at a Solution

I solve the resulting diferential equation, but don't know constant value. I believed that it was -3

One of the things that the problem request if to find a expresion for v1(t), v2(t). I substituted i(t) (diferential equation solution) in the integral form of capacitor voltage formula, well that was easy, but another incise in the problem is to prove that v1(inf)=v2(inf), with the constants from the last integration it is impossible.

 

[gneill]

Homework Statement

There's a circuit, with a capacitor C1, Resistor R1, and another capacitor C2.
In t=0 ; C1 is charged with 2 V and C2 with 1 V
The value of resistor is 1 ohm, C1= 1 F C2=0.5 F

Homework Equations

Kirchoff voltage law.
Capacitor voltage at any given time. (integral form)

The Attempt at a Solution

I solve the resulting diferential equation, but don't know constant value. I believed that it was -3

One of the things that the problem request if to find a expresion for v1(t), v2(t). I substituted i(t) (diferential equation solution) in the integral form of capacitor voltage formula, well that was easy, but another incise in the problem is to prove that v1(inf)=v2(inf), with the constants from the last integration it is impossible.

Is there a circuit diagram to go with this problem? There are several ways to connect three components, and various polarities for the charges on the capacitors.

 

[1f5]

RCC picture

upload picture

Later i discovered that I have a mistake with voltage law, then i resolve the DE and had Ce^(-t/r)
After that i make a sim, and see that the current in t=0 is -1A and tends to zero when t goes to infinity. So the function must be -e^(-t).
(r1=equals 1).

I saw voltages too, but i can't figure from which function they come.

 

[gneill]

The initial current is unlikely to be negative if initially v1 > v2. Also, how do you arrive at a time constant of 1s? By inspection we can see that the current loop has C1 and C2 in series with a resistance R. What's the effective capacitance for C1 and C2 in series? The time constant should then resolve to RC_eff when you solve your differential equation.

Perhaps you should show more of your steps used to solve the DE.

 

[1f5]

Yes, you were right.

 

[gneill]

Yes, you were right.

Don't let the initial potentials on the capacitors fool you into making wrong choices regarding potential drops due to current flow through them. Whichever plate of a capacitor the current flows INTO with be the + plate as far as the potential drop for the differential equation is concerned.

If you want to make it more obvious, note that you can model a pre-charged capacitor as an uncharged capacitor in series with a voltage supply: