Circuit Theory Question (KCL/KVL/Dependent Source)

In summary, the problem is that the student is trying to solve for the current in the middle branch of a series circuit and doesn't know how to go about it. They try using voltage division but it doesn't work. They eventually find a way to solve for the current using Ohm's law and substitute in the values given.
  • #1
RoKr93
21
0

Homework Statement


Here's the problem:

Find the equivalent conductance Geq and then the equivalent resistance Req "seen" by the current source Is in the circuit in terms of the literals R1, R2, and gm.

Figure:
2013-06-16214425_zps81aea588.jpg



Homework Equations



Ohm's Law: V = IR

KVL: V1 + V2 + ... Vn = 0 for closed loops

KCL: I1 + I2 + ... In = 0 going in an out of a node

Voltage Division: V1 = Vsource * (R1/(R1+R2))


The Attempt at a Solution



I wasn't really sure how to go about this one. I know that Req = Vs/Is, so I set about trying to find a way to get that in terms of the given values, but to no avail- I don't know whether to treat this as a series circuit or parallel based on the independent source (since if it's parallel one of the paths is just the dependent current source with no resistors).

I tried using voltage division to solve for Vx, but I don't really know what good that will do me, or if I even can do that in this situation.

I'd really appreciate some direction here. Thanks.
 
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  • #2
Consider writing KCL (nodal analysis) for the top node. The node potential will be Vs...
 
  • #3
So correct me if I'm wrong, but if I do KCL on the top node, I get Is - Vs/R1 + gmVx = 0. I'm not sure how that helps...if I solve for Is and substitute, that just throws a Vx into my equation for Req.
 
  • #4
RoKr93 said:
So correct me if I'm wrong, but if I do KCL on the top node, I get Is - Vs/R1 + gmVx = 0. I'm not sure how that helps...if I solve for Is and substitute, that just throws a Vx into my equation for Req.

Your equation is not correct; You have to take into account R2 for the current in the middle branch. That current in the middle branch flows through R1 and R2, so what's an expression for the potential across R2 (Vx)?
 
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  • #5
Okay...I tried going with Is - Vs/R1 - Vx/R2 + gmVx = 0 and doing KVL on the left loop to get Vx = Vs - IsR1, then plugging all that into the Req formula. I was left with only the proper variables, which is good, but my answer (after putting in given values for the numbers) was way off, so clearly I did something wrong. I'm still not certain about my handling of KCL for the middle branch; am I missing something again there? I don't think I want to combine the two resistors because I have a defined voltage drop across one of them...
 
  • #6
RoKr93 said:
Okay...I tried going with Is - Vs/R1 - Vx/R2 + gmVx = 0 and doing KVL on the left loop to get Vx = Vs - IsR1, then plugging all that into the Req formula. I was left with only the proper variables, which is good, but my answer (after putting in given values for the numbers) was way off, so clearly I did something wrong. I'm still not certain about my handling of KCL for the middle branch; am I missing something again there? I don't think I want to combine the two resistors because I have a defined voltage drop across one of them...

The current in the middle branch passes through two resistors. They are in series. You can't avoid that. Use the total resistance of the branch to write its current.

Once you've written an expression for the current in the branch you can use that expression to determine an expression to replace Vx (use Ohm's law).
 
  • #7
I got it! Thank you very much for your help- I definitely would have kept on futilely separating R1 and R2 without it, heh. I don't know why I got it into my head that I couldn't add them up...I'll definitely have to keep that in mind for future problems.

Thanks again.
 
  • #8
RoKr93 said:
I got it! Thank you very much for your help- I definitely would have kept on futilely separating R1 and R2 without it, heh. I don't know why I got it into my head that I couldn't add them up...I'll definitely have to keep that in mind for future problems.

Thanks again.

You're welcome :smile:
 

Related to Circuit Theory Question (KCL/KVL/Dependent Source)

1. What is Kirchhoff's Current Law (KCL) and how is it applied in circuit theory?

Kirchhoff's Current Law states that the algebraic sum of all currents at a node in a circuit is equal to zero. This means that the total current entering a node must equal the total current leaving the node. This law is applied in circuit theory to analyze the behavior of circuits and to determine unknown currents.

2. Can you explain Kirchhoff's Voltage Law (KVL) and its importance in circuit theory?

Kirchhoff's Voltage Law states that the algebraic sum of all voltages around a closed loop in a circuit is equal to zero. This means that the sum of all voltage drops must equal the sum of all voltage rises in a closed loop. KVL is important in circuit theory because it allows us to analyze the behavior of circuits and to determine unknown voltages.

3. What is a dependent source in circuit theory and how does it differ from an independent source?

A dependent source is a circuit element whose value depends on the values of other circuit elements. It can be either voltage-dependent or current-dependent. In contrast, an independent source is a circuit element whose value does not depend on any other circuit element. Dependent sources are often used in circuit analysis and design to model real-life components such as transistors and amplifiers.

4. How do you use KCL and KVL to solve a circuit with multiple loops and nodes?

To solve a circuit with multiple loops and nodes using KCL and KVL, you need to first label all the nodes and loops in the circuit. Then, you can apply KCL at each node to write equations for the unknown currents at that node. Next, you can apply KVL to each loop to write equations for the unknown voltages in that loop. Finally, you can solve the resulting system of equations to determine the values of all the unknown currents and voltages in the circuit.

5. How does the concept of superposition apply to circuits with multiple independent sources?

The principle of superposition states that the total response of a linear system is equal to the sum of the individual responses caused by each input acting alone. In circuit theory, this means that the total voltage or current in a circuit with multiple independent sources can be found by considering each source separately and then adding the resulting voltages or currents. This method is useful for simplifying complex circuits and can be applied to both DC and AC circuits.

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