Mesh Currents with Differential Equations

In summary, the conversation discusses the use of mesh currents and differentiation in solving a problem. There is confusion about the physical current and the mesh current for a specific resistor, and the person is seeking help in understanding the problem. However, solving differential equations is not necessary for this particular problem, as the focus is on the behavior of a charged and discharged capacitor.
  • #1
madbo517
4
0
I've attached a picture of the problem statement, figure, and of my work so far.

I'm trying to use mesh currents and then differentiate it, but I really have no idea if I'm on the right track.

Also, I don't understand why i1 isn't just V/R (The physical current is the mesh current for R1, right?).

As you can tell, I'm pretty lost.
Would appreciate any help offered :)
 

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  • #2
Because the problem only asks for what's happening at $t=0$ and $t=\infty$, you won't actually have to solve any DE's for this problem. Remember what a charged and discharged capacitor look like, right? So you can use that knowledge to determine the answers to the questions asked.
 

Related to Mesh Currents with Differential Equations

1. What are mesh currents and why are they important in circuit analysis?

Mesh currents are the currents that flow through individual loops in a circuit. They are important in circuit analysis because they allow us to simplify complex circuits into smaller, more manageable parts. This makes it easier to apply Ohm's Law and Kirchhoff's Laws to solve for unknown voltages and currents.

2. How do you calculate mesh currents?

Mesh currents can be calculated using Kirchhoff's Voltage Law (KVL) and Ohm's Law. First, assign a direction to each mesh current and label the voltage drops across each component. Then, apply KVL to each individual mesh and solve for the unknown currents. Finally, use Ohm's Law to calculate the voltage drops in each component.

3. What are differential equations and how are they used in analyzing mesh currents?

Differential equations are mathematical equations that describe the relationship between a function and its derivatives. In circuit analysis, we use differential equations to describe the behavior of capacitors and inductors. By applying Kirchhoff's Laws and the equations governing capacitors and inductors, we can form a system of differential equations to solve for the mesh currents in a circuit.

4. Can mesh currents be used to analyze circuits with multiple sources?

Yes, mesh currents can be applied to circuits with multiple sources. The key is to use superposition to analyze each source separately and then combine the results to obtain the final solution. This involves finding the mesh currents for each source individually and then adding them together to get the total mesh currents.

5. Are there any limitations to using mesh currents with differential equations in circuit analysis?

One limitation is that this method can become very complex for circuits with a large number of components and sources. In these cases, it may be more efficient to use other techniques such as nodal analysis. Additionally, this method may not be applicable for circuits with non-linear components, such as transistors, which require more advanced techniques for analysis.

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