- #1
mabster
- 5
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Homework Statement
Prior to t=0, switch is in position A (for long time).
Afterward, switch is in position B.
We need to derive the equation for vc.
Homework Equations
[itex]v(t)=v(\infty)+[v(0)-v(\infty)]e^\frac{-t}{\tau}[/itex]
[itex]\tau=RC[/itex]
The Attempt at a Solution
at [itex]t=0[/itex]: [itex]v(0)=100\frac{10}{10+15}=40\,\mathrm{V}[/itex]
at [itex]t=\infty[/itex]: [itex]v(\infty)=0\,\mathrm{V}[/itex] since no current travels through open-circuit at capacitor.
[itex]R=R_\mathrm{th}=(15+10)\parallel 100=20\,\mathrm{k\Omega}[/itex]
From here, I would simply substitute the values in.
My problem is that this thévenin resistance is wrong (the correct value being 100 kΩ). I was told that it has to do with the entire bottom of the circuit being at 0 V relative to the 100 V, so the left hand loop of the circuit is disabled. I was hoping someone could give me a less hand-wavy reason that this would be the case?