7/30/2019 Physics Measurements Potentially Confusing

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P H Y S I C A L S C I E N C E S M A G A Z I N E

Potentially confusing? Dr Philip Matthews,School of Education, Trinity College, Dublin 2I would like to share with you some ideasabout measurements and concepts inphysics.1

Let us consider a measurement that most

students manage to perform successfully (after

some practice): measuring the temperature of hot water.

Suppose a student manages to read the scale on a mercury-

in-glass thermometer correctly. Perhaps surprisingly, it is

not the case that s/he has actually (literally) measured

temperature. Although we say that is what s/he has done,

a more exact description would be to say that the student

observed the height of a column of mercury in an evacuated

glass tube and has learnt to make a connection between

that measurement and the quantity we call temperature.

Likewise, if the student reads the scale correctly on anammeter s/he has not literally measured current. Our

everyday use of language in which we say that reading a

thermometer measures temperature is only a short-hand

way of speaking. Actually temperature (and current) is a

concept that has no physical existence of its own that

would permit us to make a direct measurement of it.

Temperature (and current) is an example of what is

sometimes known as a 'latent variable'the term 'latent'

meaning hidden as it does in 'latent heat'.

When we make a measurement we actually make

observations of physical quantities that we believe are good

indicators of the latent variable in question. For example,

the change in length of a column of mercury is believed to

Another aspect of using indicators is

that we can never measure them with

complete accuracythere is always an error

associated with an indicator; but the latent variable,

such as temperature, remains unsullied by such errors. We

believe, for example, that a metal rod has a definite,

unique, temperature even though we cant measure that

temperature with 100% accuracy. One can make a case for

saying that all the key concepts in physics are latentvariables, and that much of physics is about establishing

valid and reliable indicators for these variables (rather than

measuring them directly).

Why are these points important? Well, in some cases a lack

of clarity about the status of a measurement (i.e. an

indicator) and a concept (i.e. latent variable) can lead to

confusion. What I am about to say may be a littlecontroversial because I believe that just such a confusion

tends to make the topic of electricity more difficult for

students than it should be.

In particular, I think that it is true of the way we speak

about, and use, the concept of voltage. I suspect that there

is no physical quantity called voltage; rather voltage is

better understood as the unit of measurement of the

indicator for the latent variable electric potential.Suppose we connect a voltmeter across a resistor and then

connect the ends of the resistor to a battery. The battery

sets up an electric field in the resistor. The field has an

almost instantaneous effect on the charges in the resistor

and other conductors making up the circuit. Note that it is

h l i fi ld h h h I i

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the change in length of a column of mercury is believed toth l t i fi ld th t th h t It i t

P H Y S I C A L S C I E N C E S M A G A Z I N E

In the case of

electricity, it has

become common

practice to use theidea that voltage is the

cause of the

movement of charge.

In part that is the

result of the use of electromotive force (emf) as a term

that became associated with the difference in electric

potential between two points in an electric field, and emf

is measuredin volts.

In an ideal world, perhaps we should only use voltage as

the unit of the indicator/measure of electric potential. We

should say that current will flow in a circuit if there is an

electric field present giving rise to a difference in electric

potential between two points, and that difference is

measured as so many volts. (This is not the same as saying

that a current will flow because there is a voltage between

the points.) It seems to me that the way we talk aboutcircuits in terms of voltage is rather like saying that heat

will flow between two points if the centigrade is different

between the points rather than if the temperature is

different.

So where does this leave us? First, although text books

repeat the idea that voltage is the driver of current, that is

not a good representation of the physics. Rather, the

electric field drives the current, and if current flows theremust be a difference in electric potential between two

points. A voltmeter will give us a measure of that

difference in electric potential (measured in volts of

course).

Rather than giving students the idea that voltage drives the

current it would be better to focus on what a measurement

in terms of voltage does tell us.

Suppose we think about a resistor in a simple circuit with a

battery. At one side of the resistor let the electric potential

be V1 volts, and on the other side let it be V2 volts. Then we

know that a charge qwill have energy qV1 on one side of the

resistor and energy qV2 on the other side. therefore when

the charge moves through the resistor it loses energy q(V1

V2). In a fairly straightforward way that accounts for the

heat loss when current passes through any resistor. (There

is a similarity here with the change in energy when masses

move in a gravitational field.)

If a student asks what is voltage, perhaps we should say:

voltage is a unit that gives us information about electric

potential (like centigrade tells us about temperature). We

use it to calculate the energy a charge has at a point in an

electric field.

If we try to describe voltage as a push, or like water

pressure, we are just adding to confusion by trying to get

the unit of measurement (voltage) of an indicator of a

latent variable (electric potential) to serve a purpose for

which it is not designed. Such an approach is likely to add

to confusion, not reduce it. Might it not be better to leave

the pushing to the field, just as we use the idea of a

gravitational field being the cause of masses falling under

gravity?1

I am not going to be over-fussy about sign conventions, andsomewhat pedantic matters such as distinguishing batteries fromcells, when talking about electricity later on.