How Does Substitution Work in Mesh Analysis Equations?

In summary, the conversation discusses Kirchoff's Current Law (KCL) at node A and the equation i1 = i0 + i2, which represents the sum of currents entering equaling the sum of currents leaving. The participants also discuss how the equation was derived and clarify any misunderstandings.
  • #1
Novark
15
0
I understand everything up to the point which I've marked in red...

4020753639_1f2649796d_o.jpg


Can anyone explain those few lines?

I would greatly appreciate it!

Thanks.
 
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  • #2
Seems like KCL (Kirchoff's Current Law) at node A.
i1 = i0 + i2

(sum of currents entering) = (sum of currents leaving)
 
  • #3
muhandis said:
Seems like KCL (Kirchoff's Current Law) at node A.
i1 = i0 + i2

(sum of currents entering) = (sum of currents leaving)

I understand that part, but how did they derive the equation below that line?
 
  • #4
They just substituted into the equation above.
 
  • #5
muhandis said:
They just substituted into the equation above.

Oh, I see it now. I totally misunderstood the fact that they were simply substituting i0 = i1 - i2 into the third mesh equation.

Thanks :-)
 

FAQ: How Does Substitution Work in Mesh Analysis Equations?

What is mesh analysis?

Mesh analysis is a circuit analysis technique used to find the voltage and current values in a circuit. It involves creating mesh currents, which are loop currents that flow around individual components in a circuit, and using Kirchhoff's voltage law to analyze the voltage drops in each mesh.

How is mesh analysis different from nodal analysis?

Mesh analysis and nodal analysis are two different techniques used to analyze circuits. Nodal analysis is based on Kirchhoff's current law and involves analyzing the currents flowing into and out of nodes in a circuit. Mesh analysis, on the other hand, is based on Kirchhoff's voltage law and involves analyzing the voltage drops in individual mesh currents in a circuit.

What are the benefits of using mesh analysis?

Mesh analysis is useful for analyzing circuits with multiple current sources and voltage sources. It also allows for the analysis of complex circuits with multiple loops, making it a versatile technique for circuit analysis. Additionally, mesh analysis can be used to find the power dissipated in individual components in a circuit.

What are some common mistakes when using mesh analysis?

One common mistake when using mesh analysis is forgetting to take into account the direction of the mesh currents. It is important to assign the correct direction to each mesh current in order to accurately analyze the circuit. Another mistake is not properly labeling the mesh currents, which can lead to confusion and errors in the analysis.

Are there any limitations to using mesh analysis?

Mesh analysis is not suitable for circuits with dependent sources, as the analysis becomes more complex. In addition, it may not be the most efficient technique for circuits with a large number of mesh currents. In these cases, nodal analysis may be a better option.

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