What is the purpose of a voltage divider in electric circuit analysis?

[GreenPrint]

Homework Statement

Please see the picture below.

http://img23.imageshack.us/img23/2505/capturecfk.png

The title of this section of my lab is "Voltage divider". Now I have taken this class before =(. But anyways I know that there is a whole voltage divider formula for resistors in series and parallel. I however never remembered to memorize the formula because it was much easier for me to just calculate the voltage across each resistor.

We haven't gotten to resistors in this class yet or even the formula for resistors in parallel or series and how to find their equivalent resistances. Now I'm probably sure that I'll need to this information to analyze the data which I took.

The data which I was required to take required me to do this:
1) Fill in the shape with graphite from a pencil.
2) Take one DMM, set it to measure resistance, and place the red probe at A and the black probe at B.

Now I know that a DMM applies a voltage to measure resistance, so this is the purpose of doing this.

3) Take a second DMM and set it to measure voltage place the black probe at B with the other black probe.
4) Take the red probe from the second DMM and place it at the voltage contacts (the things labeled V1', V2'... V1, V2...) and measure the data.

Analyze your results.

Homework Equations

R = \frac{ρl}{A}

Where:
R = resistance
ρ = resistivity (in the case of graphite ρ≈1*10^{-5} Ωm
l = length
A = cross sectional area

A = wh

Where:
w = width
h = height (thickness of the graphite layer)

V = IR

Where:
V = voltage
I = current
R = resistance

The Attempt at a Solution

Now I'm kind of confused about the data which I received. The figure is not a complete circuit (V1' contact is not connected to V2' contact etc.). I understand that a voltage source is applied between A and B. But sense it's not a complete circuit there should be no current going through to the V1' V2'... etc contacts. Yet I can measure a voltage difference between the V1' V2'... contacts and B. Why is this?

Maybe I'm over thinking this. Circuits is a lot easier when you have an actual circuit. I however seem to be confused when I have figures and not circuits without physical wires and resistors.

Thanks for any help you can provide!

 

[Redbelly98]

You actually do have a circuit. The DVMs, their red and black leads, and the graphite form the circuit.

 

[GreenPrint]

So do I have a complete circuit though? Is current traveling down to all branches? The branches aren't connected so are the resistors (the graphite branches) really in parallel?

Thanks for any help!

 

[Redbelly98]

No, the branches are not in parallel. It's only a complete circuit where you are connecting the DVM.

It looks like the purpose of the voltmeter measurements is to measure the potential difference between points along the central, vertical path.

 

[GreenPrint]

Well as you get further away from the A and B contacts shouldn't the voltage increase because the resistance is increasing?

 

[Redbelly98]

No. If you are thinking of Ohm's Law, V=IR, what you say could be true if the current were the same through each branch to the different Vx contacts.

The main circuit (and current path) is the ohmeter DVM and the path from A to B. Very little current should go up any of the paths to the Vx contacts to where the voltmeter DVM is connected.