Engineering Circuit Voltage Dynamic Equations

[wilsondd]

Homework Statement

As part of a larger problem, I'm trying to understand the dynamic equations of the attached circuit with two capacitors and one resistor and a voltage source. When I use Kirchoff's Current Law at nodes V0 and V1, I get the following equations.

Homework Equations

See Attachment for circuit diagram

The Attempt at a Solution

When I use Kirchoff's Current Law at nodes V0 and V1, I get the following equations.

0 = (dVs/dt-dV1/dt)*C1 - (V1-V2)/R - (dV1/dt-dV2/dt)*C2
0 = (dV1/dt-dV2/dt)*C2 + (V1-V2)/R

I have a feeling that this approach is wrong though, since I can't solve the equation when C1 = C2. I would be very appreciative if someone could tell me where I'm going wrong.

 

[gneill]

Homework Statement

As part of a larger problem, I'm trying to understand the dynamic equations of the attached circuit with two capacitors and one resistor and a voltage source. When I use Kirchoff's Current Law at nodes V0 and V1, I get the following equations.

Homework Equations

See Attachment for circuit diagram

The Attempt at a Solution

When I use Kirchoff's Current Law at nodes V0 and V1, I get the following equations.

0 = (dVs/dt-dV1/dt)*C1 - (V1-V2)/R - (dV1/dt-dV2/dt)*C2
0 = (dV1/dt-dV2/dt)*C2 + (V1-V2)/R

I have a feeling that this approach is wrong though, since I can't solve the equation when C1 = C2. I would be very appreciative if someone could tell me where I'm going wrong.

If the terminals at V1 are open circuited as shown then no current can flow, so no potential drops will occur...

 

[wilsondd]

If the terminals at V1 are open circuited as shown then no current can flow, so no potential drops will occur...

Yes, but what if the voltage source is not constant?

 

[gneill]

Yes, but what if the voltage source is not constant?

No current can flow. But that doesn't mean the potential cannot change. Anything connected to the top lead of Vs will vary identically in potential w.r.t. to the bottom lead of Vs.