Dynamic Equations of a Circuit?

In summary, the conversation discusses the use of Kirchoff's Current Law in analyzing a circuit with two capacitors, one resistor, and a voltage source. The equations obtained using this approach are shown and it is mentioned that this method may be incorrect as it cannot be solved when C1 equals C2. The speaker requests assistance in identifying any errors.
  • #1
wilsondd
7
0
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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  • #2
There's no current so dV/dt is always zero.
 

1. What are dynamic equations of a circuit?

The dynamic equations of a circuit are mathematical expressions that describe the behavior of an electrical circuit over time. They take into account the various components of a circuit, such as resistors, capacitors, and inductors, and the relationships between voltage, current, and charge.

2. Why are dynamic equations important in circuit analysis?

Dynamic equations are important because they allow us to predict the behavior of a circuit over time, taking into account factors such as changing voltages and currents. They help us understand how different components interact with each other and how the circuit will respond to different inputs.

3. How do you derive dynamic equations for a circuit?

To derive dynamic equations for a circuit, we use Kirchhoff's laws and other principles of circuit analysis, such as Ohm's law and the capacitor and inductor equations. We then use these equations to create a system of differential equations, which can be solved to determine the behavior of the circuit over time.

4. Can dynamic equations be used for both DC and AC circuits?

Yes, dynamic equations can be used for both DC (direct current) and AC (alternating current) circuits. However, the specific equations used may differ depending on the type of circuit. For example, in AC circuits, we must also consider the frequency and phase of the current.

5. How important is it to have accurate values for components when using dynamic equations to analyze a circuit?

Having accurate values for components is crucial when using dynamic equations to analyze a circuit. Small changes in component values can have a significant impact on the behavior of the circuit over time. Therefore, it is important to use precise measurements and values when solving dynamic equations for a circuit.

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