Dynamic Equations of a Circuit?

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The discussion focuses on deriving the dynamic equations for a circuit containing two capacitors, one resistor, and a voltage source using Kirchhoff's Current Law. The user presents two equations based on their analysis but expresses uncertainty about their correctness, particularly when the capacitances are equal (C1 = C2). They mention that the lack of current leads to a situation where the derivative of voltage (dV/dt) is always zero, complicating the solution. The user seeks clarification on potential errors in their approach. The conversation emphasizes the challenges of circuit analysis in dynamic systems.
wilsondd
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Hello,

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.

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.
 

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There's no current so dV/dt is always zero.
 

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