Finding Equivalent Resistance in a Circuit

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Discussion Overview

The discussion revolves around finding the equivalent resistance in a circuit, specifically using node voltage analysis and test sources. Participants share their attempts at solving a homework problem and explore different approaches to calculating the current and resistance.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant describes their approach using a test source to find I norton and mentions confusion after calculating the voltage at a node.
  • Another participant suggests that the current io can be calculated as v/1Ω when a voltage supply is placed across terminals a-b.
  • Some participants question the influence of other voltages in the circuit, particularly the voltage beneath the 1Ω resistor, which complicates the calculation of io.
  • There is a discussion about the implications of an ideal voltage source and how it affects the potential difference across components in the circuit.
  • A participant expresses uncertainty about whether to continue using a test source and seeks guidance on the next steps in their calculations.
  • A later reply confirms the use of a test source and suggests writing KCL node equations to proceed with the solution.
  • One participant expresses relief after successfully solving the problem, indicating that it was challenging even for their professor.

Areas of Agreement / Disagreement

Participants express differing views on the role of voltages in the circuit and how they affect the calculation of equivalent resistance. There is no consensus on the best approach to take, and the discussion remains unresolved regarding the most effective method for solving the problem.

Contextual Notes

Participants reference specific circuit elements and their relationships, but there are unresolved assumptions regarding the circuit's configuration and the impact of various voltages on the calculations.

mnvaughn
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Homework Statement


The problem wants me to find the equivalent resistance at the terminals. Here is the circuit plus some of my work. The Answer according to the teacher is C.
http://i.imgur.com/JaW7f.jpg


Homework Equations





The Attempt at a Solution


As seen from my work, I added a test source. By doing this I'm trying to solve for I norton so i can divide the test source by I norton for the resistance. I start doing node voltage analysis at the node closest to the test voltage. From the calculations I find the voltage of the node farthest of the voltage source to be 2 volts. I then use node voltage at that node to solve for i0. I found i0 to be 3/4A however after that I'm completely lost.
 
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Surely if you put a voltage supply v across ab then the current io will be v/1Ω.
 
But isn't there a voltage at the bottom too? so it i0=v1/2i0?
 
mnvaughn said:
But isn't there a voltage at the bottom too? so it i0=v1/2i0?

If you place a voltage source across a-b, that voltage and no other will appear across the 1 Ohm resistor at the input terminals.
 
if it was that simple then why isn't the answer just 1? I'm really confused on why you disregard the voltage at the bottom. Underneath the 1ohm resister is not ground but another voltage which is 2i0.
 
mnvaughn said:
if it was that simple then why isn't the answer just 1? I'm really confused on why you disregard the voltage at the bottom. Underneath the 1ohm resister is not ground but another voltage which is 2i0.

io is the current through that "input" resistor, and is so defined by the circuit diagram. Call it R. You place a voltage source V across that resistor R and the resulting current through that resistor is V/R. It doesn't matter what the potential at b is because node a is V volts greater than that due to that voltage source. If V is an ideal voltage source, NOTHING can alter that.

Note that io is not the total current being "pushed" into the circuit by V. There are still calculations to do to find that!
 
what would be your suggestion to go from here then? Do i not use a test source? because i really don't know any other way to solve it then.
 
mnvaughn said:
what would be your suggestion to go from here then? Do i not use a test source? because i really don't know any other way to solve it then.

Yes, use a test source (I thought that was what the recent exchange concerned!).

If you place a test voltage source Vin across the input a-b, then you immediately know the current io. This gives you the controlled source values. From there look at writing KCL node equations. Start with the node that the current source flows into.
 
WOW. I'm SOOO STUPID. I did that exactly and i got it. Thanks that problem even stumped my professor in class. Thank you soooo much
 
  • #10
mnvaughn said:
WOW. I'm SOOO STUPID. I did that exactly and i got it. Thanks that problem even stumped my professor in class. Thank you soooo much

We aim to please :biggrin:
 

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