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

[bornofflame]

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

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.

 

[DaveE]

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.

 

[bornofflame]

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.

 

[DaveE]

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.

 

[bornofflame]

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"

 

[DaveE]

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).