# Mesh Analysis w/ Supermesh and "different" current direction

• eehelp150
In summary: For this particular problem I used the following notation:P = (SQRT(P*P+Q*Q))For display of complex power in general I'm partial to the rectangular form so that I can immediately see the real... and imaginary... parts. For this particular problem I used the following notation:P = (SQRT(P*P+Q*Q))
eehelp150

## Homework Statement

Find power absorbed by resistor, capacitor and inductor. Find the total complex power absorbed by all the loads.[/B]

KVL/KCL

## The Attempt at a Solution

I want to solve this using Mesh analysis. There is a supermesh where the 5A source is, so I start it like this:

How do I assign the mesh currents? I1 and I2 are going in different directions.

eehelp150 said:

## Homework Statement

Find power absorbed by resistor, capacitor and inductor. Find the total complex power absorbed by all the loads.[/B]
View attachment 107963

KVL/KCL

## The Attempt at a Solution

I want to solve this using Mesh analysis. There is a supermesh where the 5A source is, so I start it like this:
View attachment 107964

How do I assign the mesh currents? I1 and I2 are going in different directions.
You have been given reactances of the reactive elements while the sources seem to be dc. If you want to calculate the complex power, the sources must be ac. Is that the complete circuit diagram you have? Aren't the phase angles of the sources mentioned?

cnh1995 said:
You have been given reactances of the reactive elements while the sources seem to be dc. If you want to calculate the complex power, the sources must be ac. Is that the complete circuit diagram you have? Aren't the phase angles of the sources mentioned?
Sorry about that, the phase angles are 0 degrees.

eehelp150 said:
How do I assign the mesh currents? I1 and I2 are going in different directions.

You can assign mesh currents in any direction you like so long as you write the mesh equations according to the resulting definitions. That is, when you write the equations pay attention to the defined current directions. The alternative is to just apply your wrote procedure and then interpret the results in terms of the currents you "really" want. That is, extract your ##I_1## and ##I_2## from the mesh currents after solving for the mesh currents; signs imply directions.

gneill said:
You can assign mesh currents in any direction you like so long as you write the mesh equations according to the resulting definitions. That is, when you write the equations pay attention to the defined current directions. The alternative is to just apply your wrote procedure and then interpret the results in terms of the currents you "really" want. That is, extract your ##I_1## and ##I_2## from the mesh currents after solving for the mesh currents; signs imply directions.
-I1(10+j20) + 6V + I2(-j2) = 0
I1 + I2 = 5
Are these correct?

Yes, those look good!

gneill said:
Yes, those look good!
I1 = (-15-26i)/53
I2 = (280+26i)/53
Correct?

Yup.

gneill said:
Yup.
Finding the power absorbed by the inductor/resistor/capacitor is simply 6V * I? Where I = I2 for the capacitor and I1 for the resistor and inductor?

eehelp150 said:
Finding the power absorbed by the inductor/resistor/capacitor is simply 6V * I? Where I = I2 for the capacitor and I1 for the resistor and inductor?
The 6 V voltage source is not across any of the individual components. Use the currents through the components and the component impedances. Remember the DC version P = I2R? There's an AC version of that. Hint: One of the I's in I2 should be the complex conjugate.

gneill said:
The 6 V voltage source is not across any of the individual components. Use the currents through the components and the component impedances. Remember the DC version P = I2R? There's an AC version of that. Hint: One of the I's in I2 should be the complex conjugate.
So basically (I)(I*)(Z)

eehelp150 said:
So basically (I)(I*)(Z)
Correct. This works because with a little rearrangement we can see:

P = (I)(Z)(I*) = (V)(I*)

gneill said:
Correct. This works because with a little rearrangement we can see:

P = (I)(Z)(I*) = (V)(I*)
Capacitor: -j2 * I2 * I2*
Resistor: 10 * I1 * I1*
Inductor: j20 * I1 * I1*

Correct?
Total would be everything added up?

Yes, that looks fine.

gneill said:
Yes, that looks fine.
I ended up getting these values, would you mind double checking?
Resistor = -1.61 + 2.8i
Capacitor = 10.37 - 55.3i
Inductor = -5.6 - 3.21i
What is the proper way to display these values? Converting to complex power(S = sqrt(P^2+Q^2))?

Just out of curiosity, would the voltage across resistor be -I1 * 10ohm because of the direction?

eehelp150 said:
I ended up getting these values, would you mind double checking?
Resistor = -1.61 + 2.8i
Capacitor = 10.37 - 55.3i
Inductor = -5.6 - 3.21i
What is the proper way to display these values? Converting to complex power(S = sqrt(P^2+Q^2))?
Can you show your calculations in detail? I'm immediately suspicious because the power you found for the resistor turned out to be complex; Resistors have no reactance and can only dissipate real power no matter if the current is complex or not. Inductors and capacitors have no resistance and cannot dissipate real power, yet your results show them both dissipating some real power.

For display of complex power in general I'm partial to the rectangular form so that I can immediately see the real and reactive parts. But some prefer to see the magnitude of the apparent power and the power factor. When in doubt provide both.
Just out of curiosity, would the voltage across resistor be -I1 * 10ohm because of the direction?
You need to specify how you will interpret a voltage before you even calculate it. That is, establish a reference point or orientation on your circuit diagram for interpretation of the voltage. Otherwise you can only talk about the magnitude of the potential change. When we write KVL equations, for example, we agree on interpreting the potential change in light of the arbitrarily decided current direction and direction of our "KVL walk" around the loop.
In the figure below, the voltage ##V_R## across the resistor would be positive in one interpretation and negative in the other. Yet it's the same potential drop. It's all in how you define the "measurement" on the circuit diagram.

gneill said:
Can you show your calculations in detail? I'm immediately suspicious because the power you found for the resistor turned out to be complex; Resistors have no reactance and can only dissipate real power no matter if the current is complex or not. Inductors and capacitors have no resistance and cannot dissipate real power, yet your results show them both dissipating some real power.

For display of complex power in general I'm partial to the rectangular form so that I can immediately see the real and reactive parts. But some prefer to see the magnitude of the apparent power and the power factor. When in doubt provide both.

You need to specify how you will interpret a voltage before you even calculate it. That is, establish a reference point or orientation on your circuit diagram for interpretation of the voltage. Otherwise you can only talk about the magnitude of the potential change. When we write KVL equations, for example, we agree on interpreting the potential change in light of the arbitrarily decided current direction and direction of our "KVL walk" around the loop.
In the figure below, the voltage ##V_R## across the resistor would be positive in one interpretation and negative in the other. Yet it's the same potential drop. It's all in how you define the "measurement" on the circuit diagram.

View attachment 108066
Forgot to use conjugate.
New values:
Resistor: 3.2W
Capacitor: -56.3 VAR
Inductor: 6.4 VAR

Yes, that's much better!

## 1. What is Mesh Analysis and how does it differ from other circuit analysis methods?

Mesh Analysis is a method used to analyze electrical circuits. It differs from other methods such as nodal analysis in that it uses the concept of loops or meshes in the circuit to determine the unknown currents and voltages.

## 2. What is a Supermesh and when is it used in Mesh Analysis?

A Supermesh is a combination of two or more individual meshes in a circuit. It is used when there is a current source that is shared by two meshes, making it impossible to write separate equations for each mesh. In this case, a Supermesh equation is written to take into account the shared current source.

## 3. Can the direction of current in a mesh affect the results of Mesh Analysis?

Yes, the direction of current in a mesh can affect the results of Mesh Analysis. If the current direction is assumed incorrectly, the resulting equation and solution will also be incorrect. It is important to carefully label the current direction in each mesh during the analysis.

## 4. What are the advantages of using Mesh Analysis over other methods?

Mesh Analysis is advantageous in that it is a systematic and straightforward method to analyze a circuit. It also takes into account the direction of currents, which can be useful in solving circuits with multiple current sources. Additionally, it can be used to analyze circuits with both independent and dependent sources.

## 5. Are there any limitations to using Mesh Analysis?

One limitation of Mesh Analysis is that it can only be used to solve circuits that can be represented by meshes or loops. It cannot be used for circuits with no current sources or those that cannot be simplified into a series of meshes. Additionally, for complex circuits, the number of equations and variables can become overwhelming and difficult to solve.

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