Is Ohm’s Law ‘Universal’?

©2019 L A Waygood

Ohm’s Law is one of the most fundamental ‘laws’ in electrical engineering, and most students and electricians believe that it is ‘universal’ —i.e. it applies to all conductors, circuits, and electronic components, under all circumstances.

In fact, this is NOT the case! Ohm’s Law is not ‘universal’, and there are more conductors, circuits, and electronic components that DON’T ‘obey’ Ohm’s Law, than there are that do!

There is also a widespread belief that Ohm’s Law can be summarised in the following simple equation:

I=UR

… where I represents current, U represents potential difference, and R represents resistance.

By extension, and based on this equation, many believe that Ohm’s Law can be expressed as, ‘The current passing through a circuit is directly-proportional to the applied voltage, and inversely-proportional to the resistance’.

The above definition, in fact, is NOT the accepted definition for Ohm’s Law. In fact, Ohm’s Law makes no mention of resistance at all!

Ohm’s Law, then, is by no means a ‘universal’ law! Not many circuits or electronic components actually ‘obey’ Ohm’s Law! The equation, described above, does not, in fact, represent Ohm’s Law at all, but is derived from the definition of the ohm! So the above definition is quite incorrect!

So, what is the accepted definition of Ohm’s Law?

Ohm’s Law states that ‘the current flowing in a conductor is directly-proportional to the potential difference applied across its ends, providing the temperature and other physical characteristics remain constant.’

Ohm’s Law explained

In the 19th century, after conducting a great many experiments, a Rhinelander, teacher Georg Simon Ohm, concluded that under strictly-controlled conditions, the current passing through a metal conductor was directly-proportional to the voltage applied across that conductor.

Considering that there were no standard measuring instruments in those days (Ohm had to design his own) and neither were there any units of measurement for current or voltage (the ampere and volt didn’t exist at that time!), this was actually a remarkable experiment. And it was Ohm himself that coined the term, ‘resistance‘, to describe the opposition to the flow of current.

The ‘strictly-controlled conditions’ specified by Ohm included maintaining a constant temperature throughout his experiment. But it was not restricted to just this; it was also important, for example, not to bend or otherwise distort the conductors during the course of the experiment.

Repeating Ohm’s experiments in a school or college laboratory is very straightforward, and most students will have performed it at one time or other during their science lessons.

The simple experiment involves applying incrementally-increasing voltages across a conductor (or, more usually, a resistor of some kind), and recording the resulting value current for each increment. If the result of this experiment is a straight-line graph (of current against voltage) passing through the origin, then Ohm’s Law is confirmed. A straight-line graph is evidence of proportionality.

However, in most cases, the result will be a curved line. For example, if we were to use tungsten (the metal from which lamp filaments are manufactured), as the voltage applied to it increases, it gets hotter. As it gets hotter, its resistance increases, and the resulting graph will be a curve —evidence of a lack of proportionality, meaning that Ohm’s Law does NOT apply!

Those conductors or electronic devices that obey Ohm’s Law are, thus, describes as being ‘linear‘ or ‘ohmic‘, whereas those that don’t are described as ‘non-linear‘ or ‘non-ohmic‘. And there are FAR more ‘non-linear’ than there are ‘linear’.

For Ohm’s Law to be ‘universal’, then current must remain proportional to voltage for variations in voltage. In the case of tungsten, this is clearly not the case, so tungsten does NOT ‘obey’ Ohm’s Law.

And it’s NOT just tungsten that doesn’t obey Ohm’s Law. Any metal whose resistance is affected by temperature will not obey Ohm’s Law! And most electronic devices do not ‘obey’ Ohm’s Law, either. Take the following characteristic curve (operating curve) for a tunnel diode, as an extreme example:

Between points A-B, the graph is a straight line, so the device obeys Ohm’s Law (it’s ‘ohmic’) over that part of the curve. But, between points B-C, the line is curved, so it no longer obeys Ohm’s Law (it’s ‘non-ohmic’). Between points C-D, not only is it a curve, but it is a negative curve, so it contradicts Ohm’s Law —i.e. as the voltage increases, the corresponding current decreases! And, finally, between points D-E, the graph is a positive curve so, again, it doesn’t obey Ohm’s Law.

A tunnel diode is a rather extreme example of an electronic device that doesn’t obey Ohm’s Law. But other electronic devices, including simple diodes, also don’t fully-obey Ohm’s Law.

So, Ohm’s Law is NOT a universal law. It does not apply to all devices nor does it apply in all circumstances. In fact, there are far more conductors and electronic devices that don’t obey Ohm’s Law than there are that do!

This led to one correspondent (Glenn Elert, ‘The Physics Hypertextbook’) to write: ‘Ohm’s Law isn’t a very serious law. It’s the “jaywalking” of physics! Sensible materials and devices obey it, but there are plenty of rogues out there that don’t!’

Of course, the ratio of voltage to current (for a d.c. circuit, at least) is called ‘resistance‘. We are all familiar with the equation:

R=UI

This equation is always true, whether a device obeys Ohm’s Law or not. But it ONLY applies at any given point on the device’s characteristic curve. It cannot be used to predict the resistance elsewhere on that same curve (unless, of course, it is a straight-line curve).

So, is it time to relegate Ohm’s Law to the dustbin of history? Possibly. But a revised definition might make it more accurate:

Ohm’s Law is only true ‘when the current flowing in a conductor remains directly-proportional to the potential difference applied across its ends, for variations in that potential difference.’

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