How to Find Power Delivered by a Dependent Voltage Source Using Node Analysis?

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Discussion Overview

The discussion revolves around finding the power delivered by a dependent voltage source using node voltage analysis in an electrical circuit. Participants are attempting to derive equations and clarify their approaches to solving the problem, which involves multiple components and relationships between voltages and currents.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant expresses difficulty in solving the problem and shares an initial equation for node voltage analysis, which they believe is incorrect.
  • Another participant suggests that the equation should include a zero in the second term and notes the presence of two resistors in the branch with the dependent source.
  • There is a proposal to adjust the equation to include a different coefficient for the dependent source's term.
  • Participants discuss the relationship between the current Io and voltage V1, with one participant stating Io = -v1/100.
  • One participant mentions their calculated values for V1 and Io, but expresses uncertainty about how to find the power in the dependent source, referencing a specific answer from a textbook.
  • A later reply prompts for clarification on the voltage and current of the dependent source, suggesting the use of the power formula p = VI.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the correct formulation of the equations or the method to find the power delivered by the dependent source. Multiple competing views and adjustments to the equations are presented, indicating ongoing uncertainty.

Contextual Notes

There are unresolved mathematical steps and dependencies on the definitions of the variables involved, particularly regarding the relationship between Io and V1. The discussion reflects various interpretations of the circuit components and their interactions.

sofree
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need help to solve this problem using node analysis

find the power deliverd by the dependent voltage source

http://i170.photobucket.com/albums/u270/weiqiangt/Photo213.jpg


need to use node voltage analysis


i tried using this equation: (v1-160)/10 + (v1/100) + (v1-150 Io)/ 20

but it looks like the ans is wrong
 
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sofree said:
need help to solve this problem using node analysis

find the power deliverd by the dependent voltage source

http://i170.photobucket.com/albums/u270/weiqiangt/Photo213.jpg


need to use node voltage analysis


i tried using this equation: (v1-160)/10 + (v1/100) + (v1-150 Io)/ 20

but it looks like the ans is wrong

There are two resistors in the branch containing the dependent source: 20 ohm and 30 ohm.
The current Io is a function of V1 and the 100 ohm resistor.
Finally, you must write a zero in the second term of your equation.
 
you mean my equation will look like this:

(v1-160)/10 + (v1/100) + (v1-150 Io)/ 20 = 0

Io - v1/100

then what about my constraint equation? i really don't know how to do it
 
sofree said:
you mean my equation will look like this:

(v1-160)/10 + (v1/100) + (v1-150 Io)/ 20 = 0

Io - v1/100

then what about my constraint equation? i really don't know how to do it

Nope!
You should have
(v1-160)/10 + (v1/100) + (v1-150 Io)/ 50 = 0
Io = -v1/100

What constraint equation?
 
i use this equation (v1-160)/10 + v1/100 + (v1-150 io)/50 = 0

then

io = -v1/100

my v1 = 100V and io = -1A

need to find the power in the dependent source... but it seems with this equation i cannot get the ans...

the actual ans is 750W from electric circuit 8th edition by nillsson riedel
 
sofree said:
i use this equation (v1-160)/10 + v1/100 + (v1-150 io)/50 = 0

then

io = -v1/100

my v1 = 100V and io = -1A

need to find the power in the dependent source... but it seems with this equation i cannot get the ans...

the actual ans is 750W from electric circuit 8th edition by nillsson riedel

What is the voltage of the dependent source?
What is the current delivered by that source?
p = VI.
 

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