# Nodal and Mesh mismatch...where am I going wrong

• DFrentzen
In summary, the conversation discusses using both mesh analysis and nodal analysis to determine the current ia in a given circuit. While mesh analysis results in a value of 1.71mA, nodal analysis gives a value of 2.25mA. The issue with nodal analysis is identified to be in the substitution for v1. The conversation then discusses justifying this substitution and expressing v1 in terms of the current passing through the v1 resistor. Eventually, the correct value for current is obtained through this approach.
DFrentzen

Given the circuit diagram above, I am interested in finding the current ia. Using mesh analysis, I determined it to be 1.71mA, but nodal analysis results in a value of 2.25mA. Solution attempts provided below. I think the issue is in my nodal analysis approach.

Mesh Analysis..I1 is the left mesh, I2 the right mesh.

Nodal analysis attempt...current calculation at the bottom.

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For the node equation, check your substitution for v1: Note that the 6 V source is connected through a resistor to the reference potential.

I tried to take that into account on one of my attempts, the voltage v1 as 3-v provides the correct value for current. I was unsure if I'm on solid ground to do that.

You're on the right track. But how to justify your substitution?

Consider that you have a term in your node equation for the current that passes through the "v1" resistor. How would you express v1 in terms of that current?

gneill said:
You're on the right track. But how to justify your substitution?

Consider that you have a term in your node equation for the current that passes through the "v1" resistor. How would you express v1 in terms of that current?

I see v1 given as

Which allows me to plug in and

Looks good.

Thank you.

## 1. What is nodal and mesh mismatch?

Nodal and mesh mismatch is a phenomenon that occurs when there is a discrepancy between the number of nodes and meshes in a circuit. This can happen due to an incorrect circuit analysis or a mistake in drawing the circuit diagram.

## 2. How does nodal and mesh mismatch affect circuit analysis?

Nodal and mesh mismatch can lead to incorrect results in circuit analysis, as it can create an imbalance in the equations used to solve the circuit. This can result in incorrect voltage and current values being calculated.

## 3. What are the common causes of nodal and mesh mismatch?

The most common causes of nodal and mesh mismatch include incorrect circuit diagrams, missing or extra components in the circuit, and mistakes in labeling the nodes and meshes. It can also occur due to errors in solving the circuit equations.

## 4. How can I avoid nodal and mesh mismatch?

To avoid nodal and mesh mismatch, it is important to carefully draw and label the circuit diagram. Double-checking the circuit analysis and equations can also help identify any mistakes. Using software programs for circuit analysis can also reduce the chances of nodal and mesh mismatch.

## 5. Can nodal and mesh mismatch be corrected?

Yes, nodal and mesh mismatch can be corrected by identifying and fixing the errors in the circuit diagram or analysis. It is important to carefully review the circuit and make sure all components are correctly connected and labeled. Using alternative circuit analysis methods, such as superposition or Thevenin's theorem, can also help in correcting nodal and mesh mismatch.

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