# What does having the v in the center, with the positive near the top wire and negative near the bottom wire mean in this circuit diagram?

I understand that the symbol on the left hand side of that middle branch is a current controlled current source, and the symbol on the right is a current source.

What does it mean to have the CCCS on the left, the CS on the right, with the v in the middle, and + and - on top and bottom, respectively?

Does the whole branch, having a v in the middle describe some kind of circuit that I don't know about? Can this circuit be redrawn? Perhaps as:

I'm sorry for the poor redrawing.

Thanks for any clarification.

• Concerning the redrawing, don't forget that the lines in the drawing are ideal wires: they have no resistance and no inductance. As long as all the same points are connected together, the two circuits are the same. You could move R1 to the right, move R2 between the two sources, or pretty much anything else as long as what's connected to what stays the same. So, yes, your redrawing is okay. The result is exactly the same as the original circuit. The original is easier to understand, though; having the two sources grouped as in your redrawing is okay, but misleading. – Pete Becker Feb 9 '15 at 16:24
• "v" is probably something referred to in the text of your problem. There's nothing in the circuit that depends on it. The same goes for $i_6$. – Fizz Nov 17 '15 at 3:08

I hope you are familiar with the concept of independent and dependent sources. Still, let me explain it here. Voltage sources and current sources are basically classified as independent and dependent:

A dependent source is one whose value depends on some other parameter in the circuit. In your circuit, the current source on left side, with a diamond shaped symbol is a dependent current source. The current supplied by this source will be 2Ix (two times the value of current flowing in the branch on top right side)

On the other hand, an independent source always maintains a value which does not depend on any other parameter in the circuit. The 24mA source on right side will constantly supply 24mA, irrespective of the activities happening in other sections of the circuit.

Now, coming to your question, this is nothing but four elements in a simple parallel connection. There is nothing mysterious about the voltage v. As we know, the voltage across each element in a parallel connection will be same, this v can be considered as the voltage drop across R1, which is same as the voltage drop across R2. + and - symbols indicate the polarity of voltage drop. After solving, if v turns out to be positive, it means that top side of R1 and R2 is at a higher voltage than the bottom side.

And yes, you can redraw the circuit as you have done. And for practical purposes, you can consider this as a single sources of value (24mA+2Ix).

Circular you redraw is correct meaning of v at the center and + above and - below means drop in voltage with mentioned polarities there

• Thanks for the answer. Knowing that I can redraw it like that helps me understand what it's representing. – Nathan Lutterman Feb 9 '15 at 9:26

I think it's just to clarify that the top wire is considered to have a higher potential than the bottom wire. So for a simulation tool, you would connect the bottom wire to ground.

The v is just to indicate the voltage between top and bottom wire.