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

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  • Thread starter bornofflame
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  • #1

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.
 

Answers and Replies

  • #2
DaveE
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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.
 
  • #3
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
 
  • #4
DaveE
Gold Member
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596
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.
 
  • #5
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
"
 
  • #6
DaveE
Gold Member
789
596
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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