Monday, May 23, 2011


Nowadays high school and university students use voltmeters and ammeters to demonstrate Ohm's law. These devices were not available in Ohm's time! (Moreover, these devices rely on laws (including Ohm's law) not known at the time.) How did Ohm do it? Suggest experiments (using only equipment available in 1826, or similar present-day equipment) showing that:
(a) "voltage" is proportional to "current";
(b) for fixed "voltage", the "current" is proportional to the cross-sectional area of the wire and inversely proportional to its length.

The solution:

As a voltage source we can use batteries. Ohm first used "chemical batteries" but those had very short life-time, i.e their electromotive force (EMF) varied during the experiment. Eventually, he used a thermocouple as a voltage source. The voltage, or more correctly the EMF, was therefore N*E where N is the number of batteries connected in series and E is EMF of a single battery. If the resistance of wire was X, and internal resistance of the battery was r, then the current I was given by


Current can be measured by placing a magnetized needle hanging on a string at certain fixed distance from the wire. Since we are not supposed to know exactly the angular dependence of the magnetic force, we will simply for each current twist the string on which the needle hangs until the needle returns in its position before the current began flowing. The angle by which the string was twisted is proportional to the force momentum, and thus measures the strength of the current. (Of course we assume that forces are indeed proportional to the current.)

We will begin the experiment by keeping the same wire (the same X) and changing N. By plotting 1/I versus 1/N, we will establish r/E, and will establish the "voltage-current" relation of the Ohm's law. Now, by lengthening the wire of making its cross section larger we can investigate dependence of resistance on geometry of the wire. (Of course we cannot measure the actual absolute values of the resistance, but all we need is the dependence on length and cross section area...) Ohm published his results on geometry dependence of X in Journal fur Chemie und Physik, 46, p. 160 (1826).

Nice short description of Ohm's work in its historic context can be found in the book History of Physics (Storia della Fisica) by Mario Gliozzi.

Comment: Groshaus suggested to measure the voltage by attaching one of the leads of the battery to electroscope. Can it be done with sufficient accuracy?

My Stamp Collecting Blog

Counter Added January 1, 2011

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The A index [ LOW is GOOD ]

  • 1 to 6 is BEST
  • 7 to 9 is OK
  • 11 or more is BAD

Represents the overall geomagnetic condition of the ionosphere ("Ap" if averaged from the Kp-Index) (an average of the eight 3-hour K-Indices) ('A' referring to amplitude) over a given 24 hour period, ranging (linearly) typically from 1-100 but theoretically up to 400.

A lower A-Index generally suggests better propagation on the 10, 12, 15, 17, & 20 Meter Bands; a low & steady Ap-Index generally suggest good propagation on the 30, 40, 60, 80, & 160 Meter Bands.

SFI index [ HIGH is GOOD ]

  • 70 NOT GOOD
  • 80 GOOD
  • 90 BETTER
  • 100+ BEST

The measure of total radio emissions from the sun at 10.7cm (2800 MHz), on a scale of 60 (no sunspots) to 300, generally corresponding to the sunspot level, but being too low in energy to cause ionization, not related to the ionization level of the Ionosphere.

Higher Solar Flux generally suggests better propagation on the 10, 12, 15, 17, & 20 Meter Bands; Solar Flux rarely affects the 30, 40, 60, 80, & 160 Meter Bands.

K index [ LOW is GOOD ]

  • 0 or 1 is BEST
  • 2 is OK
  • 3 or more is BAD
  • 5 is VERY VERY BAD

The overall geomagnetic condition of the ionosphere ("Kp" if averaged over the planet) over the past 3 hours, measured by 13 magnetometers between 46 & 63 degrees of latitude, and ranging quasi-logarithmically from 0-9. Designed to detect solar particle radiation by its magnetic effect. A higher K-index generally means worse HF conditions.

A lower K-Index generally suggests better propagation on the 10, 12, 15, 17, & 20 Meter Bands; a low & steady Kp-Index generally suggest good propagation on the 30, 40, 60, 80, & 160 Meter Bands.

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