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

• Engineering

## 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.

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DaveE
Gold Member
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.

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
Gold Member
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
"

DaveE
Gold Member
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).