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.

 

[rezeew]

As a scientist, it is important to approach problems with a critical and analytical mindset. In this case, it seems that the equations derived using Kirchoff's Current Law may not be entirely accurate or may be missing some key elements. It is possible that the circuit may have some non-ideal components or may not be operating under steady-state conditions, which could affect the equations. Additionally, the equations may need to be modified to account for the initial conditions of the circuit.

To accurately solve this problem, it may be helpful to use other circuit analysis techniques such as nodal analysis or mesh analysis. These methods take into account the voltage and current relationships in the circuit and can provide a more comprehensive understanding of the dynamic behavior.

Furthermore, it may be beneficial to double-check the circuit diagram and ensure that all components and connections are accurately represented. Small errors in the circuit could lead to significant discrepancies in the equations.

In conclusion, it is important to approach circuit analysis problems with caution and to consider all aspects of the circuit before deriving equations or attempting to solve them. It may also be helpful to seek guidance from a mentor or consult additional resources to gain a better understanding of the problem at hand.