**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**

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