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2005
Wheatstone's Bridge
Tom Greenslade
Kenyon College, greenslade@kenyon.edu
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“Wheatstone’s Bridge”, The Physics Teacher, 43, 18-20, 2005
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Wheatstone's Bridge
Thomas B. Greenslade Jr.
Citation: The Physics Teacher 43, 18 (2005); doi: 10.1119/1.1845984
View online: http://dx.doi.org/10.1119/1.1845984
View Table of Contents: http://scitation.aip.org/content/aapt/journal/tpt/43/1?ver=pdfcov
Published by the American Association of Physics Teachers
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Wheatstone’s Bridge
Thomas B. Greenslade Jr., Kenyon College, Gambier, OH
T
he arrangement of four resistors, a source of
emf, and a galvanometer, known as Wheatstone’s bridge, has been in existence for more
than 170 years. The only other piece of apparatus
with its staying power is Atwood’s machine. Now that
it has reached mature status, it seems only fitting to
describe its origin, analysis, circuit topology, and past
and future uses.
Charles Wheatstone
Charles Wheatstone (1802–75)1 was one of a number of British Victorian-era physicists who worked
in many fields. Wheatstone’s early scientific interests
lay in acoustics. His inventions of the concertina (a
miniature accordion with an octagonal cross section,
played with buttons on either end) and the kaleidophone2 date from his twenties. The latter instrument
is a straight or bent wire with a mirror mounted on
the end still used to demonstrate Lissajous figures.
The rotating-mirror technique, suggested by
Dominique Arago in 1838 as a way to measure the
velocity of light in air and in water, was proposed by
Wheatstone in an 1834 paper in which he described
measuring the speed of an electrical impulse along a
wire.3 The spark from a Leiden jar was observed in
the rotating mirror as it jumped across three spark
gaps separated by long lengths of wire, and the spreading out of the images by the mirror provided the calibrated time base.
In England, Wheatstone is regarded as the inventor
of the telegraph. Unlike the familiar American pattern
of Morse on-off signals being sent over a single wire,
18
the telegraph system that he patented with William
F. Cooke (1806–77) in 1837 used a magnetic needle
that swung to the left and to the right to give the code
indicating the letters.
I am a maker of black-and-white stereoscopic cards,
and thus value Wheatstone’s pioneering work on the
stereoscopic effect.4 His paper on the subject was published in 1838, the year before the announcement of
the first photographic processes by Daguerre and Fox
Talbot, and so is illustrated with stereoscopic
drawings.
Wheatstone’s Original Design
Charles Wheatstone’s 1843 Bakerian lecture5 to the
Royal Society in London, “An account of several new
Instruments and Processes for determining the Constants of a Voltaic Circuit,” is a surprisingly modern
paper on electrical measurements. In it he discusses
the idea of resistivity, applies Ohm’s law in a number
of ways, and calculates the resistance of circuit elements in series and parallel. With a little bit of translation into modern nomenclature, this paper could be
given to present-day students as a guide to making
electrical measurements. He also gives two methods
for measuring resistance: the bridge and the rheostat
technique.6
The last part of the paper deals with “The Differential Resistance Measurer,” now known as Wheatstone’s
bridge. Figure 1, from the original paper, shows the
arrangement of four conductors in the form of a diamond, and this layout has become the normal one for
bridge circuits to this day. It has been suggested that
DOI: 10.1119/1.1845984
THE PHYSICS TEACHER ◆ Vol. 43, January 2005
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Fig. 1. Wheatstone’s original form of the bridge circuit, from
the original paper.5
Wheatstone owned a service of Blue Willow china
with diamond-shaped cross-hatching on the side of
the footbridge in the decoration. Wheatstone also
used this diamond pattern in the telegraph instrument
that he developed with Cooke. While it is possible to
draw the circuit with the four resistors on two parallel
lines, the diamond pattern is a reminder that we are
dealing with a bridge.
Wheatstone used a differential method devised by
Christie 10 years earlier.7 This is the familiar circuit
in Fig. 1. The emf (the “rheomotor” in Wheatstone’s
nomenclature) was attached between points Z and
C, and the galvanometer between points a and b.
The four copper wires are of the same length. With
jumpers across the gaps cd and ef, the pivoted arm m,
sliding on the wires, was adjusted to give zero deflection on the galvanometer. The unknown resistance
was placed across one of the gaps, and a calibrated
rheostat across the other gap was adjusted until the
galvanometer again read zero. The rheostat thus had
the same resistance as the unknown. Wheatstone did
not develop the familiar equation for the ratios of the
resistance arms at the balance point.
Today we are accustomed to dealing with resistances in the kilo-ohm range, since we use emfs of a
few volts and want to measure milliamperes of current. Wheatstone was more interested in the resistance
of relatively short lengths of wire, and so the use of
lengths of copper wire in the ratio arms was perfectly
reasonable. To give a sense of scale, the entire bridge
was mounted on a board 14 in long and 4 in wide,
and the wire was 1/20 in in diameter. Figure 2 shows
a Wheatstone bridge, drawn in a rectilinear form
instead of the usual diamond shape. The familiar
expression for the balanced bridge is R1/R3, = R2/R4.
The derivation is learned by most introductory students, most of whom will never use Wheatstone’s
THE PHYSICS TEACHER ◆ Vol. 43, January 2005
Fig. 2. Rectilinear circuit for the Wheatstone bridge.
bridge. It is, however, a useful circuit for pedagogical
reasons.
Commercial Bridges
While it is standard practice to make up a bridge
out of an unknown and three resistances (at least one
of which must be adjustable), it is much easier to use
a self-contained instrument. The example in Fig. 3
is a Type-S Portable Resistance Test Set by Leeds and
Northrup of Philadelphia, and it cost $90 in 1940.
Quite a number of these are still in existence in physics departments, and readers are urged not to throw
Fig. 3. Portable test set form of Wheatstone’s bridge
by Leeds and Northrup; in the Greenslade collection.
19
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them away but to use them.
There are dozens of other designs of the bridge,
some looking like battleships in brass!
The Wheatstone Bridge in the
Present-Day Curriculum
How should we use Wheatstone’s bridge today?
Typically it has fallen out of the experimental curriculum and is covered only in the theory portion of the
course. Thus, it has suffered the same fate as Atwood’s
machine,8 which started out as a lecture demonstration in the 18th and 19th centuries, became an experiment for a while, and now is used mainly as a vehicle
in the classroom for illustrating Newton’s second law.
Doing a basic experiment with Wheatstone’s bridge
can be rather dull. You set up the device, make a measurement of an unknown, and pass on. This would be
a good deal more interesting if the resistance changed
in some interesting way, and if the students had some
input in making the samples. For example, the students could be given a number of spools of insulated
copper wire of various gauges, asked to cut off various lengths from different spools and measure their
resistances, and make a plot of resistance as a function
of length/cross-section area. Or, the students could
simply be asked to find out how resistance depends on
sample length and cross-section area.
About 20 years ago I used the bridge in an experiment for first-year students on the temperature coefficient of resistance of copper wire. The students were
told to cut off a meter of #42 copper wire and remove
the insulation with formic acid (we used very small
bottles held upright in wooden blocks for safety).
They soldered the ends of the wire to heavy wires connected to the bridge and learned something of soldering in the process. The wire was doubled over, wound
around the bulb of a thermometer, and insulated
with layers of masking tape. The resistance doesn’t
change a great deal over the range from ice water to
about 70C, but with a little care a fine straight line is
obtained for a resistance as a function of temperature
graph, and the value for the temperature coefficient of
resistance obtained from the slope agrees well with the
handbook value.
Recently I discovered that the students in my sophomore/junior electronics class knew nothing about
the bridge and so I added an experimental segment
20
about it. This group of students will never use a bridge
to measure resistance, but they might use it for control
purposes. Therefore, they measured the off-balance
voltage across the galvanometer as a function of the
unbalancing resistance. Like most phenomena, this
gives a straight line when not pushed too far. They
were reminded that the unbalancing element might be
a temperature sensor, and the off-balance signal used
in a feedback circuit to keep the temperature constant.
As the reader can see, the bridge circuit is one of
my favorite pedagogical tools, both in the classroom
and in the laboratory. This paper is homage to an old
friend, and an invitation to my colleagues to use it
once more.
References
1. My favorite reference on Wheatstone and his career is
Brian Bowers, Sir Charles Wheatstone (Her Majesty’s
Stationery Office, London, 1975).
2. Thomas B. Greenslade Jr., “19th century textbook
Illustrations LI: The kaleidophone,” Phys. Teach. 30,
38–39 (Jan. 1992).
3. Thomas B. Greenslade Jr., “The rotating mirror,” Phys.
Teach. 19, 253–255 (April 1981).
4. Thomas B. Greenslade Jr., “The first stereoscopic pictures of the Moon,” Am. J. Phys. 40, 536–540 (1972);
Merritt W. Green III and Thomas B. Greenslade Jr.,
“Experiments with stereoscopic images,” Phys. Teach.
11, 215–221 (1973).
5. Charles Wheatstone, “An account of several new instruments and processes for determining the constants
of a voltaic circuit,” Philos. Trans. Roy. Soc. Lond. 133,
303–324 (1843).
6. For the rheostat technique, see Thomas B. Greenslade
Jr., “19th century textbook illustrations XXIII: The
rheostat,” Phys. Teach. 16, 301–302 (May 1978).
7. Samuel Hunter Christie, “Experimental determination
of the laws of magneto-electric induction in different
masses of the same metal, and of its intensity in different metals,” Philos. Trans. Roy. Soc. 123, 95–142
(1833).
8. Thomas B. Greenslade Jr., “Atwood’s machine,” Phys.
Teach. 23, 24–28 (Jan. 1985).
PACS codes: 01.65, 06.30L, 41.20
Thomas B. Greenslade Jr. is professor emeritus in the
physics department at Kenyon and a frequent author for
The Physics Teacher.
Kenyon College, Gambier, OH 43022;
greenslade@kenyon.edu
THE PHYSICS TEACHER ◆ Vol. 43, January 2005
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