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.


  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.