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

• Engineering
• bornofflame
In summary, the conversation discusses a problem involving a circuit and the values of R1 and G (gain). The problem is based on a similar problem in a textbook and additional information is provided in the textbook version. The conversation includes a discussion on the solvability of the problem and clarifies that the numerical answers for R1 and G have already been obtained. It is stated that the problem is solvable, but not uniquely, due to the configuration of the circuit. The conversation ends with a summary of the question being asked.
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.

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.

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).

## 1. What is the purpose of solving for R1 and G in this circuit?

The purpose of solving for R1 and G in this circuit is to determine the voltage and current values in the circuit. This information is important for understanding the behavior of the circuit and making any necessary adjustments or modifications.

## 2. How do you calculate R1 and G in this circuit?

R1 can be calculated using Ohm's Law, which states that resistance (R) is equal to voltage (V) divided by current (I). G can be calculated using the voltage and current values in the circuit, as well as the properties of the VCCS (voltage-controlled current source).

## 3. What is the significance of Vs in this circuit?

Vs represents the voltage source in the circuit. It is the source of electrical energy that powers the circuit and provides the necessary potential difference for current to flow through the circuit.

## 4. How do you determine the values of Vs and VCCS in this circuit?

The values of Vs and VCCS are typically given in the circuit diagram or can be measured using a voltmeter and ammeter, respectively. Vs is the voltage value of the source, while VCCS is a constant value determined by the properties of the voltage-controlled current source.

## 5. Can this circuit be simplified using equivalent resistances?

Yes, this circuit can be simplified using equivalent resistances. By combining resistors in series or parallel, the overall resistance in the circuit can be reduced, making it easier to calculate the values of R1 and G.

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