Mesh analysis with dependent voltage source

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Discussion Overview

The discussion revolves around solving a circuit problem using mesh analysis, specifically focusing on the complex power delivered by a source, the power factor of the total load, and the nature of the power factor (leading, lagging, or unity). The conversation includes attempts at calculations, clarifications regarding circuit components, and considerations for expressing results.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant attempts to solve for currents using mesh analysis, presenting equations for two meshes.
  • Another participant points out that the controlled source is a current source, suggesting the use of a supermesh or an additional variable for proper analysis.
  • Further contributions confirm the correctness of earlier calculations and provide additional equations involving the currents.
  • Participants discuss how to find the complex power supplied by the source, with suggestions to use the current and voltage from the source.
  • There is a discussion about the power factor, with references to the power triangle and calculations for complex power.
  • One participant questions whether to convert complex power to VA form, while another suggests it is not necessary unless specifically asked.

Areas of Agreement / Disagreement

Participants generally agree on the calculations presented, but there is some uncertainty regarding the representation of the controlled source and the necessity of converting complex power to VA form. The discussion remains unresolved on whether the power factor is definitively leading, lagging, or unity.

Contextual Notes

There are unresolved assumptions regarding the definitions of the components in the circuit and the specific requirements for expressing power. The discussion also reflects varying preferences for notation in complex power calculations.

eehelp150
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Homework Statement


Find the:
-Complex power delivered by source
-Power factor of total load
-Is the power factor leading, lagging, or in unity?[/B]
upload_2016-10-24_22-39-39.png


Homework Equations


KVL/KCL

The Attempt at a Solution


I want to solve this via mesh analysis to get currents.
Mesh1: -10V + V1 + 0.75V1 = 0
V1 = 40/7V
4I1 = 40/7
I1 = 10/7 A

Mesh2: -0.75V1 = I2(1-j1.5) = 0
I2(1-j1.5) = 0.75 * 40/7
I2 = 30/(7(1-j1.5))

Did I do this right?
 
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The controlled source depicted is a current source, not a voltage source. So either employ a supermesh or introduce another variable to represent the potential across it (and you'll need another equation so that you have as many equations as variables in your equation set).
 
gneill said:
The controlled source depicted is a current source, not a voltage source. So either employ a supermesh or introduce another variable to represent the potential across it (and you'll need another equation so that you have as many equations as variables in your equation set).
-10V + 4(I1) + I2(1 - j1.5) = 0
I2 = 3/4V1 + I1
V1 = 4(I1)

Are these correct?
 
Yes, those look good.
 
gneill said:
Yes, those look good.
i1 = 0.8 + 0.6i
i2 = 3.2 + 2.4i
correct?
 
That looks good, too.
 
gneill said:
That looks good, too.
How would I find complex power supplied by the source?
 
eehelp150 said:
How would I find complex power supplied by the source?
Use the current supplied by the source and the source voltage.
 
gneill said:
Use the current supplied by the source and the source voltage.
Is current supplied by source I1 - 3/4V1?
How would I find the power factor?
 
  • #10
Presumably the source referred to is the 10 V voltage source. It supplies just I1.

For the power factor you need to look at the power triangle. The complex power will give you the two "legs" of the triangle.
 
  • #11
gneill said:
Presumably the source referred to is the 10 V voltage source. It supplies just I1.

For the power factor you need to look at the power triangle. The complex power will give you the two "legs" of the triangle.
So complex power = 10 * I* = 10 * (0.8 - 0.6i)?
S = 8-6i
Power factor = P/S = 8/10 = 0.8 leading? (Q<0)
Does this triangle look right?
upload_2016-10-26_23-5-16.png
 
  • #12
eehelp150 said:
So complex power = 10 * I* = 10 * (0.8 - 0.6i)?
S = 8-6i
Power factor = P/S = 8/10 = 0.8 leading?
Yes. Also, write 'j' instead of 'i' in the imaginary part of the complex form (e.g
S=8-j6). That's a convention followed in order to avoid confusion with the symbol 'I' for current.
 
  • #13
cnh1995 said:
Yes. Also, write 'j' instead of 'i' in the imaginary part of the complex form (e.g
S=8-j6). That's a convention followed in order to avoid confusion with the symbol 'I' for current.
Can (should) I convert to VA form? (sqrt(P^2+Q^2))
 
  • #14
eehelp150 said:
Can (should) I convert to VA form? (sqrt(P^2+Q^2))
Not necessary if apparent power is not asked. You can keep it in the complex form.
 

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