Phys Educ. 20 1985. Prlnted In Northern Ireland.
Electromotive
force
A C Rose-lnnes
Students, when dealing with electric circuits, often
have difficulty in understanding the distinction
betweenpotential difference (PD) andelectromotive force (EMF). Yet it is important to understand
this distinction, which occurs in several situations:
the potential difference at the terminals of a battery
may be less than its EMF-Kirchhoff‘s second law
tells us that around any closed circuit the sum of
the EMFS (a) equals the sum of the PDS ( V ) :
but if we cannot distinguish between PDS and EMFS,
how do we know on which side of the equation to
put any particularvoltage?Forexample,
is the
voltage across an inductor a PD or an EMF?
In my experience, any difficulty usually arises
from misunderstanding
a
of the
nature
of
electromotive force rather than
a
failure to
understand the nature of potential difference.
EMF
and the ‘electropump’
The potential difference between two points is
defined as the work which must be done to transfer
unit charge from one point to the other. Potential
difference is the result of the electrostatic attraction
and repulsion which charges exert on each other.
Alistair Christopher Rose-Innes is Professor of
Physics andElectrical
Engineering, University of
Manchester Institute of Science and Technology. His
M A (Physics) and D Phil were obtained at Oxford
and his DSc from Manchester University. He was
previously a Principle Scientific Officer in the Royal
Naval Scientific Service and his researchinterests
include low-temperature techniques and solid-state
physics, especially superconductivity and contact
electrification. He has
written
three books and
numerous articles in scientifc journals on these
subjects.
0031-9120/85/060272+035’2.25
0 1985 The
Institute of Physlcs
a
A
B
c
D
b
A’
B’
C’
D’
Figure 1 Analogy between a fluid-flow and b electric
current
The distinction between PD and EMF in a circuit is
probably best explained by looking at an analogous
fluid circuit. Consider the sequence of water-filled
pipes shown in figure la: if the pressureat A is
greaterthan the pressure at D, water willflow
through from A to D. Conversely, a flowof water
forced through from A to D will create pressure
drops across each pipe, the pressure on the right
hand side of each pipe becoming less than that on
the left handside.
The electrical equivalent is
shown in figure lb: potential is analogous t o
pressure and electric current to fluid flow. So, if the
potential at A’ is greater than the potential at D’,
current flows from A’ to D’ and
potential
a
difference will be set up across each resistor.
How do we, however, keep the current flowing
through the resistors? To keep the current flowing
we must maintain a potential difference V , - VD
across the resistor chain. Let us return to the fluid
analogue. To keepthe fluidflowingwe
needa
pump (figure 2a). What does a pump do? A pump
is a device which uses some form of energy to
create apressure difference between its inletand
outlet. For example, a pump may use the energy
from an electric motor or the kinetic energy of the
wind. The analogouselectric circuit is shown in
figure 2b; current
through
the resistors is
maintained by a battery which maintains a potential
difference between its positive and negative
terminals. We see that a battery is an ‘electropump’
which uses the energy of a chemical reaction to
maintain the potential difference between its
terminals.
Thereare, of course, many kinds of electropump: the dynamo which uses the rotational kinetic
energy of a motor
to
maintain the potential
difference between its terminals, the photovoltaic
cell (solar battery) which uses the energy of light
etc, etc (Kip 1962, Harnwell 1949). Electromotive
force is a potential difference which is produced by
the conversion of other f o r m ofenergy (kinetic
energy, light energy etc).
Of course, virtually all electropumps have an
internal
resistance,
r say, so when they are
delivering current, I , the PD, V , betweentheir
output terminals will be less than the EMF 8 by the
potential drop produced across the internal
resistance by the current I,
V = 8 - Ir.
Note that in a circuit a potential difference only
appears across a component if a current is flowing
through it. Thus in figure 2b there will only be a
voltage drop across the resistors if the switch S is
closed, but an electropump
produces
an EMF
whether or not current is passing through it. Note
also that where there is a potential difference, the
direction of the current isalways from the higher
potential to the lower potential, butcurrent may
flow either way with respect to an EMF. In figure 3
thecurrent
flows through the two batteries in
opposite directions relative to their EMFS.
g*
Figure 3 Direction of current [with respect to EMFS g
R
L
l
An example
In Kirchhoff's equation (1) we put all the EMFS on
one side and the PDS on the other. It is usually easy
to see which are EMFS and which are PDS but there
are cases where it is not completely obvious. A
careful application of the concepts of EMF and PD as
given above will always resolve the problem.
Consider,for example, a circuit containing an
inductor, as shown in figure 4. If we want to know
what current flows round this circuit at time t after
the switch has closed we can apply Kirchhoff's law.
8 is clearly the EMF of the battery and goes on one
side of the equation and the voltage drop IR across
R is clearly a PD and goes on the other. But what
about the voltage across the inductor?
Figure 2 Electric battery b as an analogue of a fluid
Pump a
L
1
Pump
Pump
I
%
S
Figure 4 Circuit containing inductance
The voltage across an inductor is generated by
the changing magnetic flux threading the coils; in
other words, an inductance can be considered as an
electropump using the energy of a magnetic field to
create apotentialdifference.
We may, therefore,
regard the voltage across it as an EMF and put it on
the left side of equation (1). On the other hand, the
voltage across an inductor is duetothe
current
through it,t so this looks like a PD and should go on
the right handside of equation (1). Is there a
paradox?No; we can treatthe voltage across an
inductor as either an EMF or a PD. If, first, we
consider the inductor as an electropump, theEMF it
generates is - L dlldt, so we would write Kirchhoff's
equation for the circuit in figure 4 as:
8 + (-L dlldt) = RI.
(2)
On the other hand, we can consider the inductor
as a passive circuit element across which a current
produces a PD equal to LdIldt.Kirchhoff's equation
for the circuit of figure 4 can therefore be written:
8 = R I -k L dIldt.
It can be
seen
that this equation is exactly
equivalent toequation(2).In
practice, in circuit
problems it is usually more convenient to treat the
voltage across an inductance as a PD equal to
i The magnitude of the voltage is proportional to the rate
of change of the current.
273
Phys
Educ. 20 1985Printed In Northern Ireland
LdIldt, though it can be seen that treating it as an
EMF equal to -LdI/dt is equally valid. No problem
arises, of course, if the nature of both PD and EMF
are fully understood.
T o summarise; EMF is produced by an electropump, a device which uses non-electrical energy to
maintain a potential
difference
between
its
terminals. The EMF is produced whether or not the
‘pump‘ is delivering current. If this concept of an
electropump is firmly understood, there should be
no difficulty in understanding the natureof EMF and
its relationship to PD.
References
Kip A F 1962 Electricity and Magnetism (New York:
McGraw-Hill)
Harnwell G P 1949 Principles of Electricity and
Electromagnetism (New York: McGraw-Hill)
The refractive
index of thin
solid films
S K J AI-Ani and J Beynon
A fundamentalopticsexperiment
in theschool/
undergraduate physics laboratory is theinvestigation of the dispersion of visible light using a prism
spectrometer. The refractive index, n, of the prism
material can be calculated for various wavelengths
with the help of the familiar relation
n = sin [ ( A
Computers in physics
teaching
The Computational Physics and Education Groups
of The Institute of Physics are planning a series of
joint meetings on topics of common interest to both
Groups. Thefirst meeting, on ‘The use of
computers in mainstream physics teaching’, will be
held at the Universityof Essex on Thursday 9
January 1986 and will be a full day meeting
(10.30-17.00) organised jointly by Dr D Tilley
(Education Group) and DrH Liddell (Computational Physics Group). The meetingwill consist of a
mixture of invited and contributed talks, poster
presentations and demonstrations by manufacturers, publishers and individuals who have developed
interesting software in this area.
The provisional programme includes the
following speakers and topics:
‘The Computer Board initiativeon facilities for
teaching’ by R J Elliott (Oxford) or J Forty
(Warwick); ‘Computer assisted texts’by R A
Harding (Cambridge); ‘Physics students and
computers’ by G Toombs (Nottingham); ‘Microcomputer perturbation theory’by J Killingbeck
(Hull); and ‘Software for undergraduatephysics’ by
A D Boardman (Salford).
Further details can be obtained from the
Meetings Officer, The Instituteof Physics, 47
Belgrave Square, London SWlX 8QX (tel.01-235
6111).
0031-9120/85/060274~04$2.250 1985 The lnstltute of
Physlcs
+ Dmi,)/2]/sin( A / 2 ) ,
(1)
where A is therefractingangle of theprismand
Dminis theangle of minimum deviation. Figure 1
shows the variation of n with wavelength obtained
with an ordinary ‘student’ optical spectrometer and
a sodium discharge lamp as source.
With reasonable care it is possible to verify that n
and A satisfy a simplifiedCauchy relationof the form
n=L
+ MA-2,
(2)
where L and M are constants characteristic of the
prism material.Equation
( 2 ) is alsoplotted
in
Salwan Al-Ani, a graduate of Baghdad Universim,
gainedan MPhil from the University of Surreyin
1981and
a doctorate from Brunel University in
1984. His research
interests
are in theoretical
physics-the kinetic theory of gases and amorphous
thin film properties-and he is the author of various
articles in this field.He now lectures at Baghdad
University.
John Beynon is a lecturer in physics and co-director
of the physics and electronics joint honours course at
Brunel University. He gained a doctorate from the
University of Wales, was a CEGB Research Fellow
at University College, Swansea and has worked with
The Signals Research and Development Establishment. His main research interests are thin films and
vacuum technology andhis
publications include
Conduction of Electricity in Gases
(1971 London:
Harrap) and Physics andChance (1974 London:
Hutchinson Educational).