Circuit Voltage Dynamic Equations

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Discussion Overview

The discussion focuses on the dynamic equations governing a circuit comprising two capacitors, one resistor, and a voltage source. Participants explore the application of Kirchhoff's Current Law to derive equations at specific nodes within the circuit, addressing the implications of circuit conditions such as open terminals and the nature of the voltage source.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents equations derived from Kirchhoff's Current Law at nodes V0 and V1, expressing uncertainty about the validity of the approach, particularly when C1 equals C2.
  • Another participant notes that if the terminals at V1 are open circuited, no current can flow, implying that no potential drops will occur.
  • A subsequent reply questions the assumption that no current can flow if the voltage source is not constant, suggesting that potential can still change despite the lack of current.
  • Further clarification is provided that while no current can flow, the potential connected to the voltage source can vary, affecting the circuit dynamics.

Areas of Agreement / Disagreement

Participants express differing views on the implications of an open circuit at V1 and the behavior of the circuit under varying voltage conditions. The discussion remains unresolved regarding the validity of the initial equations and the effects of the voltage source.

Contextual Notes

Participants have not reached consensus on the correct interpretation of the circuit dynamics, particularly concerning the conditions under which current flows and the behavior of the voltage source.

wilsondd
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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.
 

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wilsondd said:

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...
 
gneill said:
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?
 
wilsondd said:
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.
 

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