The Circular Reasoning of “Verifying” Ohm’s Law in School

The experimental set-up

A common experiment done in high school is to verify Ohm’s law. Ohm’s law, or rather one part of it, states that the current through a resistance is directly proportional to the difference in potential (voltage) between its two ends.

The diagram below represents the circuit that is often used for verifying this relationship. A fixed resistance R is connected to a battery in series with a variable resistance (rheostat). A voltmeter is connected in parallel to R and an ammeter in series.

The resistance of the rheostat is varied to get different sets of values of voltage and current which may then be plotted on a graph to show that they are proportional.

Do voltmeters actually measure potential difference?

The fallacy arises from how voltage is measured. The analog voltmeters commonly used are actually modified galvanometers in which a magnetic needle is deflected depending on the strength of the current. In fact, voltmeters make use of Ohm’s law to convert the needle’s deflection to a voltage reading in the first place!

Digital multimeters work in a different way, but they too depend on current that’s drawn from the circuit, and their calibration too likely involves the application of Ohm’s law at some point.

It is therefore apparent that it makes little sense to “verify” Ohm’s law using measuring instruments that are themselves designed on the basis of the same law.

Axiom for Ohm, Hypothesis to be tested for Kohlrausch

What Georg Simon Ohm did was to define a new quantity called potential difference for a circuit element. Electric potential is essentially an electrostatic quantity and Ohm used it to explain what happened in a circuit with a continuous current.

Ohm himself never intended to try to measure this potential difference. However, Rudolf Kohlrausch did exactly that, a quarter of a century later.

Kohlrausch used a special, sensitive electrometer to directly measure the electrostatic potential difference between the ends of a resistance and showed that it was indeed proportional to the current.

His work was published in 1849 as a paper titled Die elektroskopischen Eigenschaften der geschlossenen galvanischen Kette (The Electrostatic Properties of a Closed Galvanic Circuit). Unfortunately, an English translation of the paper does not seem to be available.

Reference

  1. Nahum Kipnis. A Law of Physics in the Classroom: the Case of Ohm’s Law
  2. R. Kohlrausch. Die elektroskopischen Eigenschaften der geschlossenen galvanischen Kette. Annalen der Physik vol 78

Nahum Kipnis on the 7 Benefits of a Historical-Investigative Approach to Science Teaching

In the introduction to his book Rediscovering Optics, physics educator and history of science scholar Nahum Kipnis lucidly summaries what he considers to be the main benefits of a historical-investigative approach to science teaching – an approach in which historical experiments are repeated and the findings reconstructed by the students. I paraphrase them below.

1. Doing something “real”

Most laboratory work in school can be described as “cookbook experiments”. There are pre-determined procedures to be followed with expected pre-determined outcomes. The students are assessed on how well they can follow the procedure and analyse the data obtained. It has very little in common with a real scientific investigation.

Recreating a historical experiment, on the other hand, places the activity in a context. The students can be introduced to the question that was being investigated by scientists in the past, and can carry out the experiment as if they were trying to find the answer themselves. Reliving an important event in the history of science may also be exciting to many students.

2. As smart as Galileo and Newton!

Students tend to ask questions and harbour preconceptions that are often remarkably similar to the ones early scientists did. In repeating historical experiments, the students can also independently arrive at conclusions similar to those put forward by these scientists. This could enable students to see themselves as scientists, and boost their self-confidence and interest in learning science.

3. Doing, not watching

This is not specific to the historical-investigative approach, but generally students engage better if they themselves carry out an experiment rather than simply watch it demonstrated by the teacher. In this approach, however, it becomes imperative since the students are trying to find an answer to a question on their own.

4. The scientific method in practice

By carrying out a series of experiments and deducing scientific concepts independently, the students are enacting a microcosm of the discoveries made in the past. This would give them a taste of how new knowledge is constructed by the interaction of theory and experiment.

5. “Obsolete” theories can help in understanding

Many old theories are based on simple models. This makes them more easily accessible than modern theories to students who are introduced to a new topic for the first time. The students can analyse and critique them while they make sense of the phenomena under study.

For example, while teaching electrostatics to class 6 students, I have found it helpful to completely sidestep the modern knowledge of subatomic particles and use the 18th century conception of two electrical fluids – resinous and vitreous.

Teachers need not feel that they are teaching something “wrong” by tapping into the potential of the old theories. History of science tells us that no theory is final.

6. Qualitative, not quantitative

Until the mid-1800s, most scientific experiments were qualitative. Many of the quantities and units that we obsess over in high school science were yet to be precisely defined. Several important physical laws were derived from rather crude measurements.

In a historical approach, this opens the door for setting up a much wider variety of experiments than the standard ones, using commonly available materials. Aspects of experimental work like precise measurements and estimation of error which are given a lot of attention in the modern labs are of much less consequence for early experiments.

7. Treasure trove of stories

History of science is full of fascinating stories that are sure to captivate students, whether they are interested in science or not. They also reveal the messy human side of science, which is totally ignored in a conventional approach that focuses on the mastery of modern scientific knowledge.

Electrostatics in Middle-School – Part 3: Early Electrical Knowledge in the Classroom

Read the previous parts if you haven’t: Part 1 Part 2

In the previous article, I briefly introduced the major developments in the knowledge of electricity up to the first half of the 17th century. So, what lessons and activities for the classroom can be designed based on this?

I intend to describe one possible approach here. I leave it to the creativity and imagination of readers who may be teachers to think of better ways. I hope you’ll come back and share your ideas in the comments if you get inspired by this and come up with other ideas to try out!

From plastic ruler to amber

Every student would invariably have rubbed a plastic ruler on hair and observed tiny paper bits flying towards it. I would tell my students that people in ancient Greece had done the same thing with amber, as a starting point for the narrative. Although amber itself is a rare and expensive material and difficult to come by, some students would have read about it and would be eager to share with the class what they knew about it.

Is it magnetism?

It might seem like a trivial thing, but asking students whether they think that this attraction happens due to magnetism is a good way to get them warmed up for scientific inquiry. The students will be forced to articulate why the attracting power of the rubbed plastic ruler cannot be magnetism. And if you’re lucky, you may even have one student in class who asserts that it is magnetism and states her reasons — then it won’t be a trivial discussion any more!

Depending on how the debate unfolds, there may be opportunities to get the students to design simple experiments to check if a rubbed plastic ruler has any properties of a magnet.

  • Does a rubbed plastic ruler have poles? Are the paper bits attracted more strongly to the ends as in the case of iron pieces to a magnet?
  • Does the rubbed plastic ruler have any directionality? Does it align in the north-south direction if suspended by a thread?

Which other materials become attracting when rubbed?

The students can then repeat William Gilbert’s experiments to find out which materials around them get this attracting power when rubbed. I would get the students to make their own simple versorium by hanging a pencil from their desks with a thread. They would then pick up every substance they could find around them and check whether they can make the versorium rotate when rubbed. Some students might start exploring the question of whether the material used for rubbing matters.

Gilbert’s versorium
(Image: Public domain)

This activity is great fun, but it also quickly reveals the difficulties and limitations of scientific inquiry in the classroom. What the students will learn from the activity depends a lot on what materials they have with them to test with the versorium.

Ideally there would be several materials that are electrics and several that are non-electrics. However, this is not so easy in practice. Apart from most plastics like polythene, PVC, etc. there aren’t too many common materials that easily become charged on rubbing. In very dry weather, you can succeed in charging candle wax, a rubber eraser and sometimes paper — enough to detect with a versorium.

One question I was faced with was whether I should choose the set of materials I wanted the students to experiment with. I could make sure that there were different kinds of electrics and non-electrics in the set. But wasn’t that cheating? Wasn’t that in a way pre-determining what the students would “discover”? Could I even say that the students were “discovering” anything?

This is a complex question and I’ll share my thoughts on it in a later post. Here, it would suffice to say that in such situations, I’ve almost always tilted towards a pre-determined outcome — mostly due to my own personal discomfort with not knowing how a class will unfold!

Attraction and repulsion

One last experiment that can be done by the students based on this part of the story is on electrical repulsion. This can be demonstrated the first time, in case the students do not stumble upon this phenomenon on their own in the limited time they have.

It is actually the same experiment with the plastic ruler, but using small bits of aluminium foil instead of paper. With bits of aluminium foil, repulsion happens in a far more noticeable way when the pieces hit the ruler. Sometimes you can even get a foil piece to dance up and down between the ruler and the table!

Students can be asked to form their own hypotheses about why the aluminium foil pieces sometimes rebounded.

Electrostatics in Middle School – Part 2: Early Knowledge of Electricity

Read Part 1 if you haven’t.

Amber and Lodestone

Since antiquity, people have been fascinated and mystified by rare materials with special properties. Two such materials were amber — a fossilised resin from extinct pine-like trees — and lodestone — an iron-containing mineral that we now recognise as permanently magnetic.

The ancient Greek (4th century BCE) knew about the property of amber to attract light objects like feathers when rubbed. They also knew that lodestone could attract small bits of iron. Amber and lodestone were often mentioned in the same breath, because their powers to attract objects were strikingly similar.

An ant preserved in amber
Image: Anders L. Damgaard. CC-BY-SA

Jerome Cardan, a 16th century Italian mathematician and physician, was one of the first to make a clear distinction between the action of amber and lodestone. He noted that rubbed amber attracted any light object while lodestone attracted only objects made of iron. He also observed that the lodestone’s attraction was the strongest at its ends (poles) while amber seemed to have no such polarity.

Such distinctions between amber and lodestone remained scattered until the end of the 16th century. It was William Gilbert — Queen Elizabeth’s physician — who first studied electrical phenomena independently. His book De Magnete (“On the Magnet”) was published in 1600. The book was mostly about magnetism, but included Gilbert’s experiments on electricity. It is ironic that electricity was discussed only as a part of one chapter on magnetic attraction, yet it established the study of electricity as a separate branch of science.

William Gilbert demonstrating electrical experiments to Queen Elizabeth.
Image: Public Domain

Not just amber

Perhaps Gilbert’s greatest contribution to the study of electricity was his discovery that not just amber, but a large number of other substances too showed similar attractive powers when rubbed. His list included precious stones such as diamond, sapphire, carbuncle, opal and amethyst, artificial materials like glass, minerals like fluorspar from the mines, fossils like belemnites, sulfur and hard sealing wax.

Gilbert coined a new term for such materials which displayed the amber effect — he called them “electrics“.

The first electrical instrument

Gilbert also invented a handy little device to identify whether a substance was an electric or not. It consisted of a thin metal needle suspended such that it could rotate freely. If a rubbed electric was brought near one end, the needle promptly turned towards the electric. He called it the ‘versorium’ – Latin for ‘turn-about’.

Gilbert’s Versorium
Image: Public Domain

The versorium enabled Gilbert to detect even electrics with very weak attracting power, because the needle needed very little force to rotate on its support. Before the versorium was invented, an electric could be identified only if it directly attracted small objects, which needed a stronger force.

Do electrics repel too?

Thus far, all the studies on electricity only mentioned the power of attraction. In 1629, an Italian scholar named Niccolo Cabeo first reported that when a light object was attracted to an electric, often it rebounded to a distance of several inches after touching the electric. This seems to have been the first observation of electrical repulsion. Cabeo found this strange behaviour hard to explain, and the rebounding remained a mystery.

No significant progress in electrical research took place for almost another 100 years. Electricity continued to arouse the curiosity of scientists during this time, and several intriguing experiments were carried out. However, given that my primary purpose is to lay out a convenient narrative for teaching, I choose to skip them here.

***

In the next article, I will examine the lessons and classroom activities that can be designed based on the early discoveries discussed so far.

Reference

Duane Roller and Duane H. D. Roller. The Development of the Concept of Electric Charge: Electricity from the Greeks to Coulomb. Harvard Case Histories in Experimental Science – Volume 2

Sparks and Giggles: Electrostatics in Middle-School — Part 1 (Prelude)

Electrostatics and the school science curriculum

Electrostatics is a topic that sits awkwardly in the school science curriculum. In fact, it is hardly a topic in itself before it is introduced in all its mathematical glory in grade 11. Until then, students normally only encounter a handful of scattered electrostatic facts and phenomena without getting the opportunity to make meaningful connections.

As a student, I had carried out the ubiquitous experiment of rubbing a plastic ruler on my hair and seen little paper bits get attracted to it. I was told that this happened because the plastic ruler had become electrically charged. I was told that there were two kinds of charges, one was called positive and the other, negative. I was also told that the same kind of charges repelled each other and the opposite kinds attracted each other.

There seemed nothing unusual about all this, and I was happy to accept it as the truth. Many years later, I realised that perhaps it was the analogy with the easily observable magnetic poles that made it so easy to unquestioningly accept the existence of two kinds of electrical charges and their behaviour. (There is a fascinating historical connection here, which I will examine in an upcoming sequel.)

As an extension, the metal-leaf electroscope was touched upon, and so too the fact that lightning was a strong discharge of static electricity. That was all the electrostatics I learnt until grade 10, and I’m sure most others did, and continue to do today as well.

The neglect of electrostatics is not surprising at all when you look at the electrical devices around. Whether it is a lamp, a motor, a heater or a computer, almost all the devices we use work on electrical currents. There is a closed circuit involved, and there is electricity in motion. There are hardly any electrical devices in daily use where electrostatic charges build up and attract tiny bits of paper (old CRT-televisions being a notable exception, of course).

A blanket on fire and electrified children on chairs!

I grew up in the humid coastal state of Kerala. It was at the age of 22 that I moved to Pune for work. There, I first experienced a dry winter — when the relative humidity could fall as low as 20%. And one night I discovered that this had other ramifications apart from having to apply petroleum jelly to avoid cracked lips.

That winter, I was using a coarse woollen blanket provided by the school to cover myself while sleeping. One night, I woke up feeling cold. The blanket had slipped off my body. As I pulled the blanket back over me, I was dazzled by an intricate web of dim yellow sparkles emanating from the blanket. There was also a faint crackling sound.

Initially I thought I was dreaming and I pinched myself to check if I was. And no, the sparkling and crackling were real!

The next day, I spoke to a friend and colleague — also a science teacher — about what I saw. He explained to me that the extremely low humidity made it possible for electrostatic charges to accumulate to very high potentials, making such brilliant discharges possible.

I came to know from him that some children in the school had found innovative ways to have fun during dry weather. They would make one person sit on a plastic chair with her legs folded up. Another person would hit the back of the chair many times with a woollen sweater. Then, when you touch the person sitting on the chair, you get a strong shock that makes you jump!

It all started with electrostatics

All this piqued my curiosity immensely and I was lucky to find two indispensable sources to learn more about electrostatic phenomena. One was the BBC Four documentary series – Shock and Awe: The Story of Electricity hosted by Jim Al-Khalili, and the other was the Harvard Case History on the development of the concept of electric charge.

And what I learned from these sources completely turned the tables on what I thought I knew about electricity. For the first 200 years or so of its development (roughly 1600-1800), ‘electricity’ meant electrostatic phenomena. There were no batteries, no motors, no devices that you would recognise today as ‘electrical’. And an awful lot was discovered about electricity during this time.

This made me wonder if it was possible to approach the teaching of electricity in school from an entirely different angle. One that paralleled the historical development of ideas, and drew on those stories of discovery.

This was 2011, I was teaching chemistry to grades 9 and 10, and I wasn’t able to actually try this out. In 2013, I left teaching to explore other areas of work. However, I did return to teaching in 2016 and this time I had grade 6 science to teach. Exactly the age group I wanted to explore electrostatics with.

In the coming posts, I intend to document my attempt at teaching electrostatics using a historical approach to eager 11-year olds.