Find Node A and B Voltage with Mesh Analysis

In summary, the conversation is about using Mesh analysis to find the voltage of Node A and B in a circuit. The equations used are V=IR and KVL, and the mesh current equations are deemed correct. The method for finding the voltages is using Ohm's law and choosing a path from the reference node. It is mentioned that multiplying (I1-I2) with a 10ohm resistor would work for finding the voltage at Node A. For Node B, the voltage is found to be 4.48 + 36.39j. However, it is also noted that adding j50 to Va would also give the correct voltage for Vb.
  • #1
eehelp150
237
0

Homework Statement


PK88BSE.png


Use Mesh analysis to find voltage of Node A and B

Homework Equations


V=IR
KVL

The Attempt at a Solution


Are my mesh equations correct?

Mesh1:
-j30V + (-j50 + 10)I1 - 10I2 = 0

Mesh2:
(10-j20)I2 - 10I1 - j50V - I3(-j20) = 0

Mesh3:
(-j20+30+j10)I3 - (-j20)I2 = 0
 
Last edited:
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  • #2
Yes, your mesh current equations look fine.
 
  • #3
gneill said:
Yes, your mesh current equations look fine.
How would I get the voltage of Node A and B?
 
  • #4
eehelp150 said:
How would I get the voltage of Node A and B?
Ohm's law. You've solved for the currents so now you can find the potentials across any components you wish. Choose a path from the reference node to the location where you wish to know the potential and sum up the PD's along the way.
 
  • #5
gneill said:
Ohm's law. You've solved for the currents so now you can find the potentials across any components you wish. Choose a path from the reference node to the location where you wish to know the potential and sum up the PD's along the way.
So if I wanted the voltage at Node A, I would multiple (I1-I2) with 10ohm resistor?
 
  • #6
eehelp150 said:
So if I wanted the voltage at Node A, I would multiple (I1-I2) with 10ohm resistor?
That would work, yes. Any path from the reference node to a would work, and that happens to be a pretty convenient choice :smile:
 
  • #7
gneill said:
That would work, yes. Any path from the reference node to a would work, and that happens to be a pretty convenient choice :smile:
I ended up getting:
14.329 < -71.74 degrees for Va
Is that right?Would Vb be: (I2-I3)*(-j20) -> 4.48 + 36.39j?
 
Last edited:
  • #8
eehelp150 said:
I ended up getting:
14.329 < -71.74 degrees for Va
Is that right?Would Vb be: (I2-I3)*(-j20) -> 4.48 + 36.39j?
They look good to me.

Note that for Vb you could also have just added j50 to Va; there is a fixed source of that amount tying them together.
 
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1. How does mesh analysis work?

Mesh analysis is a method used to analyze electrical circuits by dividing the circuit into smaller loops or meshes and applying Kirchhoff's voltage law (KVL) to each mesh. This allows us to determine the voltage drop across each element in the circuit and solve for unknown voltages.

2. What is the purpose of finding node A and B voltage with mesh analysis?

The purpose of finding node A and B voltage with mesh analysis is to determine the voltage at specific nodes in an electrical circuit. This information is important in understanding the behavior of the circuit and can be used to calculate other parameters such as current and power.

3. How do you identify the nodes A and B in a circuit?

Nodes in a circuit are points where two or more circuit elements are connected. To identify nodes A and B, you can trace the circuit and look for points where multiple elements intersect or are connected by a wire. These points will be the nodes.

4. What are the limitations of mesh analysis?

Mesh analysis is limited to circuits that can be divided into meshes and have a closed loop. It is also not suitable for circuits with dependent sources or non-linear elements. In addition, it can become complex for circuits with a large number of meshes.

5. Can mesh analysis be used to calculate the voltage at any node in a circuit?

Yes, mesh analysis can be used to calculate the voltage at any node in a circuit as long as the node is part of a mesh. However, for simplicity, it is often used to find the voltage at only a few selected nodes in a circuit.

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