Help with RC circuits SPDT switch

[asdf12312]

Homework Statement

Find v(t) after t=0, when the switch moves up

need to know if i did this right.. V(C1)=V(C2)=10V (this is same for t=0- and 0+)
V(infinity)=0V (no voltage source)

T=RC=100k(ohm)*(4uF)=0.4 sec. (i got the 4uF by putting the 2 caps. in parallel with each other, because they are in series after t=0.)

v(t)=v(infinity)+[v(0)-v(infinity)]*e^(-t/T) <-- general equation
V(t)=10e^(-2.5t)V
where i got -2.5t by dividing -t/0.4

please help!

Homework Equations

The Attempt at a Solution

 

[gneill]

Rethink your V(infinity). If both VC₁(0⁺) and VC₂(0⁺) are the same (10V at t = 0⁺), what potential difference exists to drive a current through the 100 kΩ resistor?

 

[asdf12312]

well there wouldn't be any current would there? and i thought V(infinity) would go to 0V once the voltage source gets disconected. the caps. in dc are replaced by an open circuit so i believe current would also be 0A.

 

[gneill]

well there wouldn't be any current would there? and i thought V(infinity) would go to 0V once the voltage source gets disconected. the caps. in dc are replaced by an open circuit so i believe current would also be 0A.

With no current flow, the charges on the caps cannot change...

 

[asdf12312]

sorry for the long delay, was waiting for my teacher to post homework answers because i was unsure myself.

according to this, i(t) is 0. because i think the 2 capacitors voltage cancel out? 10V-10V=0V.

 

[gneill]

sorry for the long delay, was waiting for my teacher to post homework answers because i was unsure myself.

:
:​

according to this, i(t) is 0. because i think the 2 capacitors voltage cancel out? 10V-10V=0V.

Yup. A more technically satisfying way to put it would be that because the potentials across the two capacitors are identical, the potential difference across the 100kΩ resistor is zero so that no current will flow through it. And since no current flows, the charges (and thus the potentials) on the capacitors will remain constant.