Dynamic Equations of a Circuit?

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SUMMARY

The discussion focuses on deriving the dynamic equations for a circuit comprising two capacitors (C1 and C2), one resistor (R), and a voltage source (Vs). The user applies Kirchhoff's Current Law (KCL) at nodes V0 and V1, resulting in two equations. However, the user encounters difficulties in solving the equations when C1 equals C2, indicating a potential flaw in their approach. The user seeks clarification on the correct application of KCL in this scenario.

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  • Understanding of Kirchhoff's Current Law (KCL)
  • Familiarity with dynamic circuit analysis
  • Knowledge of capacitor and resistor behavior in circuits
  • Basic differential equations
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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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