Solve for R1 and G in circuit with Vs, VCCS, and 2 resistors

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Discussion Overview

The discussion revolves around solving for the values of resistance R1 and gain G in a circuit involving a voltage source (Vs), a voltage-controlled current source (VCCS), and two resistors. Participants explore the implications of the circuit configuration and the information provided in a textbook problem, considering both theoretical and practical aspects of circuit analysis.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Exploratory

Main Points Raised

  • One participant expresses uncertainty about how to proceed with the analysis after applying Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL), particularly regarding the current value associated with Vs.
  • Another participant questions the accuracy of the schematic, suggesting that the configuration with a current source in parallel with a voltage source may render the values of G and R1 irrelevant for determining the current through the outer loop.
  • A participant claims to have numerical answers for R1 and G, stating R1 = 100 Ω and G = 0.015 A/V, derived from solving the problem as presented in the textbook, despite the textbook not providing answers.
  • One participant acknowledges the solvability of the problem but emphasizes the importance of understanding that GV2 represents a current, not a voltage, and suggests using KVL to find R1 and KCL to find G.
  • Another participant reiterates the question of whether the problem is solvable with the given information, concluding that it is not uniquely solvable due to the dependence of the outer loop current solely on GV2, which allows for multiple valid values of R1 and G without a definitive relationship between them.

Areas of Agreement / Disagreement

Participants express differing views on the solvability of the problem. While some believe it can be solved with the provided information, others argue that it cannot be uniquely determined due to the nature of the circuit configuration and the relationships between the variables.

Contextual Notes

Participants note that the problem is a simplified version of a textbook example, which includes additional information that may affect the analysis. There is also mention of the ambiguity in the circuit configuration, which complicates the determination of R1 and G.

bornofflame
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Homework Statement
Find the values for R1 and G (gain) in following circuit.
Hint: start by writing a KCL at bottom node
Relevant Equations
KCL, KVL, Ohm's Law
IMG_20200413_143837.jpg

I've gotten to the point where I've hit a roadblock and am not sure what step to take next. I started by using KCL on the bottom node as suggested by the problem, then used KVL on the left mesh, but I still have ##i_{v_s}## which I'm not sure what to equate it to, so that I can pull it out of the equations. I can't say that Gv##_2## = 20 V b/c Gv##_2## is a current value, right?

I'm also wondering if this problem is solvable as is b/c it's actually a stripped down version of a problem in our textbook: Introduction to Electric Circuits 9th Edition. James A. Svoboda. Richard C. Dorf.

The problem in the book gives additional information:
The voltage source in the circuit shown in Figure P 3.2-25 supplies 2 W of power. The value of the voltage across the 25-##\Omega## resistor is v##_2## = V. Determinethe values of the resistance R##_1## and of the gain G of the VCCS.
 
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Are you sure that you've copied the schematic correctly? The configuration with a current source in parallel with a voltage source is strange. All of the current from G can flow through Vs with no effect on the resistor branch. So it doesn't really matter what the value of G is, unless you want to know the current through the outer loop. This also means that it doesn't really matter what the value of R1 is.
 
DaveE said:
Are you sure that you've copied the schematic correctly? The configuration with a current source in parallel with a voltage source is strange. All of the current from G can flow through Vs with no effect on the resistor branch. So it doesn't really matter what the value of G is, unless you want to know the current through the outer loop. This also means that it doesn't really matter what the value of R1 is.

I've attached a screen shot of the original circuit and problem as read in the textbook. I assume that the textbook has it this way more as a study in what if or something.

Also, I don't know if this was clear, but I already have the numerical answers for each variable: R##_1## = 100 ##\Omega## and G = 0.015 A/V. I get these by solving the problem as written in the textbook. The book doesn't provide answers for the problem, but I verified my solution with other sources.

prob3.2-25.png

solved3.2-25.jpg
 
Oh, I see. I missed the part about the voltage source providing 2W.
Yes it is solvable. But I'm not sure what your question is.
You can't say GV2 = 20V, GV2 is a current, not a voltage, as you said.
You can use KVL to solve for R1, and then KCL to solve for G.
 
I'm sorry if I've convoluted this. My questions is this:
Given only the circuit and the following prompt, is this solvable?

"Find the values for R1 and G (gain) in following circuit (15 points)
Hint: start by writing a KCL at bottom node
"
 
bornofflame said:
I'm sorry if I've convoluted this. My questions is this:
Given only the circuit and the following prompt, is this solvable?

"Find the values for R1 and G (gain) in following circuit (15 points)
Hint: start by writing a KCL at bottom node
"
No, not uniquely. You can see this by inspection. Since the outer loop current is ONLY dependent on GV2, those values can be anything. You can't even find a relationship between R1 and G (i.e. given R1, you still can't solve for G).
 

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