Engineering Solve RC Circuit Switch w/ Vs=10V, R1=20kΩ, R2=100kΩ, C1=6μF, C2=12μF

[gfd43tg]

Homework Statement

2. The switch in the circuit below had been closed for a long time before it was opened at t = 0. Given that Vs = 10 V, R1 = 20 kΩ, R2 = 100 kΩ, C1 = 6 μF, and C2 = 12 μF, determine i(t) for t ≥ 0.

Homework Equations

The Attempt at a Solution

For this problem, my initial thought is that the voltage must be the same across C1 and C2, since they are open, no current runs through R1 nor R2, so the voltage across both is 10 V. Then, I use the equation for the voltage as a function of time, and get the expression. I then take the derivative and multiply by the equivalent capacitance to get my expression.

I got a negative answer, I'm not sure if this is right. It would mean the current is the opposite direction that I labeled. Would the current go from the larger capacitor to the smaller one?

 

[gneill]

If the potentials on the capacitors are identical when the switch opens, what does that tell you about the current through R2?

 

[gfd43tg]

Yes, the current is zero. Does that mean the current is zero at all times when the switch is turned off? I think my voltage expression is correct, so I just take the derivative to find the current expression.

 

[gneill]

Yes, the current is zero. Does that mean the current is zero at all times when the switch is turned off? I think my voltage expression is correct, so I just take the derivative to find the current expression.

Yes, the current is zero. No potential difference across R2 means that no current will flow. If no current flows then the potentials on the capacitors cannot change over time... what does that tell you about i(t) ?

 

[gfd43tg]

i(t) = 0 for all t?

 

[gneill]

i(t) = 0 for all t?

Yup. Well, for all t ≥ 0 that is.