## Introduction: Resistors Class - Draw Resistors Using a Pencil (Suggested Experiments Included)

This instructables is aimed at teachers trying to teach concepts in electricity, but others who like science and performing their own experiments might enjoy it as well :)

In this instructable I'll show you a nice way to introduce some concepts on resistors / conductors using simple items that all kids have - pencils!** Using pencils you can actually draw resistors** of your own design, allowing you and your students to perform almost any experiment that comes to mind, many of which cannot be done with ordinary resistors / components found at school. Also, creating resistors this way is extremely simple and so each student in class can make his own experiment even if the teacher has very limited resources.

This class should take about 45-90 minutes when teaching science to 9th-10th grades. Older students with some physics background could do it in less time. My instructions will also include some analogs between electricity and other subjects which could be more intuitive for young students.

I've also included a simple way to **estimate the thickness of a line drawn by a pencil **using nothing but the simplest tools. I think this is a nice way to show students what science is about, and how to deduce interesting stuff from your experiments!

Hope it helps!

## Supplies

You'll need:

1) One multi-tester (to measure resistance). One would be good enough for an entire class, but if you have more that would be even better.

2) Two pieces of plain paper for each student.

3) A pencil for each student.

4) A ruler for each student.

## Step 1: Resistors (Theory)

When you applied voltage across a conductor, current begins to flow. A **perfect conductor** is one which does not resist the flow of current through it when voltage is applied. Perfect conductors and not what you ordinarily see in your daily life. Instead, conductors usually have resistance.

A **resistor **is an electric component which resists the flow of current when voltage is applied across it. Simple resistors, the most common ones, obey a simple formula for their resistance (see first picture), which describes the resistance of a wire. According to the formula, resistance increases because of 3 different reasons. Resistance is measures in Ohms.

__The first factor in the formula is 'Rho'__ (the Greek letter that kind of looks like a 'p'). It is the **resistivity** of the material. Good conductors (like gold and other metals) have very low resistivity, while bad conductors (aka insulators such as plastics, wood & air) have very high resistivity. A high-valued resistor is one that resists the electric flow very much. Resistivity of wires is measured in Ohms * meters.

Analogs that could help in explaining to young students:

a) Cars driving on a road (flow of cars = electric current) while the resistivity is the condition of that road (good road vs a bumpy dirt road).

b) Flow of water through a tube (flow of water = electric current). Resistivity could be added if you put rocks and obstacles to interfere with the flow of water, or due to friction between the water flow and the tube itself. The water flow analogy is more directly related to electricity, but it could be less intuitive to some students.

__The second factor in the formula__ is the **cross-section** of the wire, marked by the letter A in the formula. A cross section is area you would measure if you sliced the resistor perpendicular to its main axis (you can find an example for what a cross-section of a cylinder looks like in the second picture). A smaller cross section would make for larger resistance. Cross sections are measured in m^2 (meters squared) = units of area.

Analogs:

a ) Cars driving on a road - the cross section would be the number of lanes. More lanes = faster traffic (less resistance).

b) Flow of water - a hose with a large diameter would let water flow more easily.

__The third factor in the formula is the length of the wire__ (or resistors) marked by the letter L. Notice that longer wires have more resistance.

The traffic / water flow analogs could work here as well! For the traffic analog I would say that longer roads make the trip for each car longer ~ the road resists the passage of cars more (this is not perfect but it is good enough in my opinion). For the water flow analog, a longer tube would resist the flow of water more due to more friction and such between the water and the hose / obstacles.

## Step 2: Connecting Resistors (Theory)

When we take two resistors and connect them, what we do is basically modify the parameters in the formula for resistance.

For example, when we **connect resistors in series** we basically make our resistor longer. For example, let's thing of two resistors of length L1. Connecting them in series would result in an effective resistor with resistance equivalent to a single resistor with length L = L1 + L1. This is why when we add resistors, we add them linearly:

R_tot = R1 + R2 + R3 +...

On the other hand, **connecting resistors in parallel **is equivalent to making the cross-section of the resistor larger. Using the analogy of traffic moving on a road is excellent here - adding more resistors in parallel to the others is just like adding more lanes going from one destiny to another. This is why adding resistors in parallel decreases the total resistance, and why the obtain the slightly less simple formula:

1 / R_tot = 1/R1 + 1/R2 + ...

## Step 3: Resistors in Series - Experiment!

Next comes the experimental part.

As most pencils are made of graphite, which is conductive, as the students draw lines on papers they are basically drawing imperfect conductors - resistors! We will use that to do some science. In this part of the experiment we will draw a 'wire' using a pencil, and measure the resistance between two points while increasing the distance between them. Basically we're changing 'L' in the original formula (longer wire).

You can draw a sketch of the experiment on the board and each student would copy it to their papers.

Ask the students to draw a line of about 10-15 cm using ordinary pencils. Pens would not work!!

The results would be most consistent if they draw the lines as evenly as possible - just run the pencil across the ruler 5-6 times (see video).

Next, mark the distance from one edge of the straight line by adding circles. Marking once every 1cm should be more than enough.

Finally, make a small table with two columns - one for the length of the wire and one for the resistance measurements. My pencil has high resistivity and so I measured the resistance in mega-ohms (1,000,000 ohms).

At this point, students would need to measure the resistance of their drawings! As students draw and measure at different rates, ask the ones that are done to use the multi-meter to measure the resistance at different wire lengths and record the results using the pre-made table. I suggest doing the next part of the experiment before moving on to analyzing the results, since students could finish that at home if time runs out.

**** The title of the paper I showed in the video should be 'Connecting Resistors in Series' !! Sorry for the confusion!**

## Step 4: Resistors in Parallel (Experiment)

In this part of the experiment we're going to connect several resistors in parallel - we're going to add more lanes between two destinations.

Draw two small squares of about 5mm or so. Leave about 40mm (4cm) between them. You'll later connect these two squares by more and more lines, each line will act as another resistor connected in parallel to the others.

Once again, draw a table to keep the results.

Using a sharp pencil and a ruler, draw a single line between the two squares. As before, try to make it as even as possible and go over it a few times. 5-6 times should be enough.

Measure the resistance between the two squares and write down the results.

Add more lines between the two squares. After each line, measure the resistance, and write the results. Try to make as many lines as possible. I could fit 6 lines using a sharp pencil.

## Step 5: Analyze the Results!

At this point, students can put the results on a graph and obtain some useful information of it! This can be done on a simple millimetric paper. If your students have access to simple graphing software (like Excel), that would make things a bit simpler, but millimetric paper works just fine.

__First, we analyze the experiment with resistors connected in parallel__. In this experiment, we changed 'L' (the length of the wire) in the formula for the resistance. This means that if we plot the resistance as a function of L, the corresponding slope of the line would give us the ratio 'Rho/A', which is the resistance of our thin wire (the pencil-drawn line) per unit length.

My results showed that the relation between resistance and the length of the wire (pencil line) is linear, which actually **validates the formula** we saw in the theoretical part! Did you find similar results? Maybe they were different? What could lead to different results?

In my case, I measured this to be about 0.3 Mega-Ohms per cm. This is an interesting quantity that teaches us about the material itself! We will use it in the bonus section to measure the thickness of lines drawn by a pencil!

__Next, we can plot the results from the second experiment.__ Recall that the formula says that R = Rho*L/A. As we add more lines we basically change A. Remember the analogy we used with cars in traffic? Adding resistors in parallel means we're adding more lanes! This explains while adding more resistors (drawing more lines) makes the current flow more easily (= lower resistance). According to the formula, the resistance should drop with as 1/N where N is the number of lines (this is true because all lines have approximately the same cross-section, and so adding more line simply increases the cross-section A by a constant factor, A_tot = A+A+A+..

This means that it would make sense to plot R as a function of 1/N. I found that plotting R as a function of 1/N leads to a linear relation, which actually** validates another part of the theory**! The relation between the resistance and the cross-section of the resistor is R ~ 1/A as predicted by the theory!

In my opinion, one of the main goals of this experiment is to show students how theoretical predictions can be tested through careful experiments. We used the simplest tools one could think of to test theory, and it was more than enough to learn plenty of new things about physics and about planning and performing our own scientific experiments.

## Step 6: ** Bonus for Advanced Students - MEASURE THE THICKNESS OF a PENCIL-DRAWN LINE **

**Have you ever wondered how thick is a line you draw on a piece of paper??**

In the previous experiments, we evaluated the ratio 'Rho/A'. But what can we do with this information next??

By measuring the ratio 'Rho/A' we can actually measure the thickness of a layer of graphite being laid when we draw on a piece of paper. We're using to think of lines on a piece of paper as being flat, but this is not true! they have a finite thickness, which we will now calculate. According the the world-wide-web the resistivity of graphite is about 30*10^-5 [Ohm*m] = 30*10^-3 [Ohm*cm] We just measured Rho/A = 3 * 10^5 [Ohm/cm]. Solving for A we find that: A = Rho/(3*10^5) = (30*10^-3)/(3 * 10^5) = 10^-7 [cm^2] = 10^-11 [m^2]. Remember that this is the cross-section of the line we just drew.

To estimate its thickness, we can divide by the line's width, which can be measured with a ruler! My lines are all about W=0.5mm wide(= 5 * 10^-4 meters). Finally, the estimated **thickness of a single line drawn by a pencil can be calculated!! H = A/(W*6) = (10^-11)/(6*5 * 10^-4) = 3.3* 10^-9 [m]** (I multiplied by 6 because I went over each line 6 times = 6 layers).

This is **just 3.3 nano meters!!** that's more than10,000 thinner than a single hair (50-100 microns). We can even estimate the number of graphite layers stacked together to make that line we seen on paper! A single layer of graphite is about 6 * 10^-10 [m] and so a line of thickness 3 * 10^-9 contains about 5 layers of graphite. That's it! 5 layers of atoms stacked on top of each other!

How cool is that? We can actually estimate the size of something so thin using just the simplest tools!

Hope you enjoyed this instructable and found it helpful! You can find more of my projects on my instructables page :)

See you soon!!

**Image of graphite was taken from physicsopenlab.org

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