# Quantitative ideas in electricity

Introductory level ideas
At introductory level, the descriptions of what happens in electric circuits are simply qualitative. It is not appropriate to discuss concepts quantitatively.

Intermediate level ideas
Defining current
Current can be described as a flow of charge measured in coulombs. You then describe and define the coulomb in terms of copper plating. You can even state that unit current, one ampere (or amp), means one coulomb per second in terms of copper plating (0.000 000 329 kg of copper carried across every second in a copper plating bath). Although that does not agree with the present fashion of defining currents by forces, it gives students a much easier way of picturing currents. They already have, from common knowledge, a strong feeling for currents as streams of little electrons, and if you bunch those electrons into large coulombs of charge you can easily persuade them to think of currents being measured in coulombs per second.

Defining Potential difference
Once students understand energy transfers, potential difference can be discussed clearly, and the volt defined as a joule per coulomb. Discussing power supplies as sources of energy, and electric charges as carriers of energy helps the beginner to understand why a current in a series circuit does not diminish as it flows through energy transfer components such as lamps. You can treat potential difference as a fundamental measurable quantity, described as energy transfer for each coulomb that passes through the region in question; e.g. the energy transferred from the battery to the lamp and hence into the environment.

It is of course unscientific fantasy to picture coulombs carrying loads of energy on their backs and disgorging some of the load in each part of the circuit, then gathering a fresh load each time they pass through the battery. Yet if you warn students from time to time that this is an artificial picture, with unrealistic details, they can use the model to develop a useful insight into potential difference.

Then resistance, which may well be more convenient in developing a professional scheme of electrical units, takes a secondary place as [potential difference]/[current] with one ohm merely defined as a name for one volt/amp. That is just dictionary work.

With these descriptions and definitions of potential difference and current, it is obvious thatpotential difference x current gives us the power, the rate at which electrical energy is transferred to thermal energy. In slang terms ‘volts x amps = watts’.

And when you generate an e.m.f. you can give a clear description of that concept too.

Advanced level ideas
In more formal treatments of electricity, unit current is chosen as the fundamental quantity (defined in terms of the force between parallel currents). Resistance is a useful derived quantity, a secondary standard that can be preserved and copied easily. Then the unit of potential difference is derived from the units of charge and energy (or current and power).

However convenient that scheme may be, it leaves the nature of potential difference itself without a clear description. Certainly at introductory level, students find ‘voltage’ a mysterious concept, often vaguely described as an electrical pressure, and frequently described as multiplying current by resistance. When the use of potential difference is extended to cases where there is no current, or cases where there is no Ohm’s law resistance, it remains very puzzling.

Developing electrical knowledge – from introductory to advanced level

There is a danger here of confusion between several different purposes in building electrical knowledge. There is the matter of careful definition of fundamental units and the deriving of secondary units; that is a matter for advanced level courses. There is the matter of describing and defining physical quantities to be measured in those units. There you need to know the physical relationship, extracted from experiments, such as thermal transfer varies as the current2, or rate of copper plating varies as the current. There are ‘operational’ definitions, in the technical sense of that word, which describe the scheme of measurement in terms of actual apparatus that could be used.

In earlier days, scientists sometimes used concepts that could not be given an operational definition. Nowadays they are more careful and try to define, or at least describe, concepts of physical quantities in terms of possible, or at least conceivable, methods of measuring them. Such definitions should yield a clear knowledge of the concept; but they do not always lead to the most convenient unit in which to measure the physical quantity. The unit chosen may be defined quite separately – you often find it was chosen earlier in the history of the subject.

There is no logical objection to defining the unit of current in terms of the mass of copper deposited per second in electrolysis, although current is formally measured in terms of force between wires or coils carrying currents.

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