Discharging Capacitor: Differential Equation in terms of Vs, C, R

[Tekneek]

Homework Statement

The voltage across the capacitor is 10V when t<0
The switch is closed at t=0

I have to find the diff eq. in terms of Vs, C, R by balancing the current at node Vc(t). But i am not sure whether the Vs is 0 or 10V at t<0

The Attempt at a Solution

I am assuming Vs = 0 at t<0 since the voltage across capacitor is 10V. Also, I am not sure what current balance at the node means...I mean when the switch is closed the current through the capacitor is the same as current through the resistor. So,

iR = iC
(Vc/R) = C (dVc/dt)

How do i write this in term of Vs? Isn't the current through the resistor Vc/R since Vs is 0 at the beginning?

 

[.Scott]

I'm not sure what you mean when you say "I am assuming Vs=0...". I think you mean that you are assuming that the voltage at the negative end of Vs is zero - which would be a fine assumption. It doesn't really matter what point you take as your "ground" or zero voltage level.

If you take Vs- as zero, then obviously Vs+ will be "Vs" and Vc(0) will be at (Vs-10v). Or, perhaps, (Vs+10V), since the polarity of the voltage across the capacitor is not explicitly specified.

 

[NascentOxygen]

The voltage across the capacitor is 10V when t<0

Are you sure this is what it says--"across the capacitor"? Can you quote precisely the wording of the question?

 

[rude man]

You have to specify the polarity of the 10V across C before proceeding with the problem. It could be +10V or -10V.

Since the source is not mentioned in the problem statement you should asume it stays at +10V for all time -infinity to +infinity.