## 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

First Prize in the

Back to Basics Contest

## 21 Discussions

17 hours ago

So, this didn't work.

But, having done this years ago, I knew it should work.

One can even make a long resistor and then use a NE555 to make a musical instrument.

So, some testing:

Out of six different pencils (all #2 HB) only one produced a barely working resistor.

Then I changed the paper. Instead of smooth copier/laser printer paper I used cheap notebook filler paper. Suddenly, half the pencils produced measurable results, one of them now a decent resistor.

Result:

1. Paper makes a difference. The smooth low-jam copier paper is probably coated and not abrasive enough. Cheaper paper or maybe even brown packing paper is probably the better choice.

2. Pencils make a difference. Even within the same hardness and brand. (Dixon #2 HB, was much more conductive than Dixon Ticonderoga #2 HB). And if I had to set it up for kids, I'd go with 2B rather than with HB.

Reply 16 hours ago

Thanks for the input! Glad you made it work eventually!

As you mentioned, it must depend on the type of pencil / paper you're using. The reasons for this are:

1) Each type of pencil is made of a different material. Some more conductive than others.

2) The combination of pencil type / roughness of paper determines to number of layers added each time you draw a line. It also makes a difference if you press hard on the paper while you draw it or not.

There are lots of factors here. I tried to make my explanations as simple as possible, but as you found out, sometimes it takes some trial and error to get things to work.

Once again, thanks a lot for your input! I'm always happy to see any comments and about 100 times happier to see that from people who actually tried the things for themselves!

Thanks!

9 days ago on Step 6

I am totally confused by your article. I have the highest license issued by the FCC in both commercial broadcast, and amateur radio. Recently I retired from 50 years in radio and television broadcasting. During some of those years I taught electronics. And after discussions with other professionals we are all confused and do not understand your techniques. As a group we find your approach totally awkward and confusing.

Reply 9 days ago

I'm sorry you feel that way! I'm not sure what do you mean by "my approach" but I'll try to give you my best answers. I'm not familiar with the FCC or amateur radio but I've been doing experiments for a few years, and I've recorded a video (see the instructable) of how I performed the experiments, and I stand behind my results.

Anyway, do you have any specific questions?

The idea I presented is simple - the stuff you have inside pencils (graphite) is conductive. This means that when you draw lines on paper, leaving layers of graphite behind, you're basically drawing conductors. Since these conductors are far from being ideal, they're not useful for making circuits, but they're very useful in studying the basics of how resistors work.

I wrote some explanations on how to relate different physical properties of a resistor such as its resistivity, its cross-section and its length, to its resistance. I then explained how you can test the theory using a drawing on a piece of paper.

To test the relation between the resistor's length and its resistance, I drew a long line and measured at different points. To test the relation between the resistor's cross-section and it's resistance, I drew two ends and connected them by more and more lines, each line adding basically increasing the cross-section.

Finally, in the last part of the experiment I used my data to estimate the thickness of a pencil-drawn line.

If you have any more questions or any constructive comments, I'd be happy to hear those.

Reply 9 days ago

NirL is a BSc, doing a masters in Physics. - So Ohm's law is not going to be totally confusing.

I do have a couple of constructive questions though.

Firstly, the over-drawing of several lines will not each add the same thickness, the interface gets smoother and less "lead" is deposited.

Secondly, the book figure for graphite resistivity is questionable - better to measure the end-to-end resistance of the whole pencil, and get a figure that way, it is powdered graphite and clay, the grain-to-grain interfaces will dominate. Certainly this will be the case on the drawn line - I can't believe it is only 6 layers thick, as graphene is almost transparent.

Given the pencil resistivity is much higher, this would predict an unrealistic extremely thin layer of pure graphite, to achieve the same high resistance.

Very soft pencils are better for close-to-graphite resistance.

Otherwise, the graphs, the concepts, all are good - it is just the final step that is too far for me.

Reply 9 days ago

I totally agree. Measuring the resistivity that way would make a lot more sense than just taking an almost random number from google. My main goal was to try and show how students can deduce stuff from their measurements. That's why I simplified things by considering all layers as having the same thickness and allowed myself to pick a number I found online - I wouldn't ask young students to do things more complicated than that, I think I'd rather sacrifice some of the validity of the results in this case. Before posting, I admitted to myself that the credibility of the actual numbers is questionable - I would get that my calculations weren't way too far off, but if one decides to measure this a better job could have been done. You're right, it's far from bein a graphene layer, and your other comments are also very true. Also, it sounds like you know a lot more about solid-state physics than I do, I only took a couple of courses, so thanks!

Thanks for spending the time to comment in depth, and for your great input!

Reply 9 days ago

No problem, just wanted to help, and to wash-out some of the unpalatable taste left by the OP - it's good work you're doing, designing paths into science.

I would suggest that doing rho.L/A on the pencil itself is no harder than doing it on the drawn line - and does introduce the concept of "least assumption" - if there is one? - using an immediately verifiable figure rather than a book figure. I guess it's eliminating systematic errors - the variability due to pencil hardness pretty much drops out.

Also the geometric similarity - Rho.L/A regardless of cross-sectional geometry, the same for a cylinder as for a thin strip.

Reply 9 days ago

The post below has a figure - 5E-5 Ohm-m, versus 30E-5 Ohm-m for graphite - so about a factor of six to be applied.

Reply 8 days ago

Thanks again. Maybe it is a good place to teach that, I like the name you picked for it too ("least assumption"), and like you pointed out it would lead to another (similar) geometry which they could test. Maybe even start by using the leads themselves like cpeoples suggested, which might be conceptually sipmler since they can actually see (and measure) the resistor's cross-section.

About rho being 5E-5 or 30E-5, the link I posted said its usually between 3E-5 to 60E-5 so I picked a simple number around the middle. I'll try to do a revised version of the last step of the instructable with my own measured values (like you suggested) this weekend:)

Hope to hear from you again!

15 days ago

My high school physics students do a very similar experiment using 2mm diameter drafting leads of different hardness grades (2B, H, 3H, 6H and 9H).

They produce a linear I v. V graph and a R v. L graph for each lead and they can compare lead hardness to its electrical resistivity. (rho is about 5 x 10^-5 Ohm m )

You can also try doing this lab with 0.7, 0.5 and 0.3 mm diameter mechanical pencil leads, but proves to be more difficult due their easily being broken.

If interested, I can prove a copy of the lab instructions.

Chris Peoples

Reply 15 days ago

That's really cool! Using a thicker pencil makes a lot of sense! I'll add your suggestion (and credit you for it!) to the instructable :) thanks!

Honestly, it all started when I tried to use a pencil to make hand-drawn circuits, but then I realized that the resistors I was drawing have very high resistance, so I started playing around with resistors instead. What are the typical resistances that your students measure using those thicker pencils? Sounds like you could reach 10-100k-Ohm if you repeat the same like a few times, is that a good guess? That's getting closer to being able to draw circuits :)

Maybe add an image of the lab instructions if that's possible? I teach physics to undergraduate students and maybe you have some cool ideas there :)

Reply 14 days ago

Hi again, below are the lab instructions (*.docx format) I use in my high school physics classes. You are welcome to use them. I only ask that you keep my name attached in case there are issues with the lab design.

For the voltmeter and ammeter I use two of the 'cheap' Harbor Freight type meters. The meters I use are two different colors (black and yellow), Yellow is configured for voltage and the black is configured for current. That way it sort of idiot proffs the lab when the students are recording the data.

For pencil leads I use the Berol Drafting Leads in various hardnesses they are available from Amazon and art supply houses.

Reply 12 days ago

Thanks for sharing your work! So you basically let the students use the drafting leads as resistors right? (not drawing on paper like I did) That's nice! I like that fact that it's easy for them to measure the length / diameter of the resistors.

Maybe you could let the more advanced students try measuring the thickness of a layer of a single drawn line like I showed here. I think it's really awesome that you can use these simple results to measure something that thin!

Thanks again!

Reply 10 days ago

Rather than measure the diameter, we use the nominal diameter (2mm) reported by the manufacturer. The big issues I have is that the leads tend to break easily and the students forget to convert the units to base quantities.

Please use the lab with your students and let me know how it works for you.

Thanks,

Chris Peoples

Physics Teacher

Sunny Hills High School

Fullerton, CA 92833

Reply 9 days ago

That makes sense, keeping things simple is often a better way to go.

It might be a while until I get a chance to use your lab, but I definitely will!

By the way, if you're new to the site maybe you should consider posting your own instructables too! Lots of teachers share their classes on the site, and if you look at the contests page you might even get a chance to win cool prizes for sharing your work, which is nice! I'll make sure to follow your just in case you do post some more.

Also, if you guys teach waves / interference at your high school, perhaps you'd like this instructable:

https://www.instructables.com/Diffraction-Experime...

The point there is that you can make a slit with variable width and show students how making the slit narrower makes the interference patterns wider (which is counter-intuitive at first).

Good luck!

13 days ago

Congratulations on being a finalist in the Back to Basics Contest!

Reply 12 days ago

Thanks a lot! That's a first for me:)

13 days ago

Wao ! What a unique concept. Loved it ♥️

Reply 13 days ago

Thanks! :)

15 days ago

Thank you! My youngest is interested in a career with electricity....this is an awesome activity for him We’re going to do this today!