Node Voltage Method: Solve for v0 in Circuit

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Homework Help Overview

The discussion revolves around using the node-voltage method to determine the voltage v0 in a given electrical circuit. Participants are exploring the application of circuit analysis principles, particularly focusing on the correct setup of equations based on the circuit's configuration.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to set up the node-voltage equations but expresses confusion about the choice of the reference node and the inclusion of current in their voltage calculation. Other participants question the correctness of the initial equations and suggest adjustments to the approach.

Discussion Status

Participants are actively revising their equations based on feedback. Some have provided corrections and clarifications regarding the relationships between voltage and current in the circuit. There is an ongoing exploration of the implications of these adjustments, but no consensus has been reached on the final value of v0.

Contextual Notes

There is mention of a missing figure that is crucial for understanding the circuit setup, which may affect the clarity of the discussion. Additionally, participants are addressing potential errors in unit conversions related to current values.

orangeincup
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Homework Statement



Use the node-voltage method to find v0 in the circuit below.

Homework Equations



i1+i2+...in=0
i=v/R

The Attempt at a Solution


So I set my reference node to the top of the middle line(above 25Ω)
Equation...
24V/(20+80)Ω+v0/25+.004A=0

Now I can solve for v0=(-.004-24/100 )* 25, v0=-6.1V

I think I did something wrong, I'm confused about a few things. How do I know where to take my reference node? Also, I'm solving for v0, yet I'm adding .004 amps to the answer. Since I'm solving for voltage, how is this possible?

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I do not see any figure.

ehild
 
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orangeincup said:

Homework Statement



Use the node-voltage method to find v0 in the circuit below.

Homework Equations



i1+i2+...in=0
i=v/R

The Attempt at a Solution


So I set my reference node to the top of the middle line(above 25Ω)
Equation...
24V/(20+80)Ω+v0/25+.004A=0

that is not correct. The current through the 20+80Ω resistors flows through the potential difference v0-24V.

ehild
 
Oh I see. I updated my solution:

(v0-24)/100+v0/25+0.004A=0

v0/100Ω+v0/25Ω=24V/100Ω-0.004A

0.05v0=.24A-.004A

v0=4.72V
 
orangeincup said:
Oh I see. I updated my solution:

(v0-24)/100+v0/25+0.004A=0

It is much better, but 40 mA=0.04 A.

ehild
 
Okay, I fixed it. v0=4.00V. Thank you.
 

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