OHM’S LAW: X= a/1,E =IR,OR I= V/R
Georg Simon Ohm (1789-1854)
歐姆定律(V=RI)
喬治．賽門．歐姆 (1789-1854)
In 1729 Stephen Gray demonstrated that a metal wire easily transmitted
“electric effluvia.” Gray was delighted with this result, and having no
measuring instruments other than his feather and a thread hanging from a
stick, felt that the electricity reached the far end of his silk-supported metal
wire undiminished in strength. Many years later, Daniel Gralath the mayor
of Dantzig, and William Henley in England both devised measurements
indicating that electricity lost some of its force (potential in today’s
terminology) as the distance from the electrostatic generator was increased.
Also, in 1771, Henley measured the conductivity of metals using his newly
invented electrometer, and ranked them from best to least: gold, brass
copper, tin, platinum, and iron.
西元 1729 史蒂芬．格瑞發現金屬線必較容易傳輸電子的＂能帶＂，格瑞很高興他能得到這個
結果。當時沒有任何的儀器他將他擁有的羽毛和線讓一個棒子帶電，他而電子卻從有皮(現在
電線的外層)且增加過強度金屬線離開。許多年以後，研究 Dantzig 的丹尼爾．葛羅勒斯和英國
的威廉．亨利都發明出測量電力(現今的專業術語叫做＂位能＂)損失的儀器，儀器量出當靜電
的移動距離靜電的損失量就會增加。亨利在 1771 年也發明了一個電表可以測量金屬線的導電
率﹐並且將她刺到的金屬線由高到低排出來：金、青銅、銅、錫、鉛、鐵。
Volta’s invention of the pile in 1800 gave new impetus to the
investigations of conductivity, because the use of the pile required
conductors to be connected to it. Oersted’s and other workers’ contributions
after 1820 gave further impetus, providing investigators with rudimentary
instruments to sense the magnetic fields surrounding the electric currents,
and thus provide an indication of Ole strength of the current.
伏特在 1800 的時候發明了一種堆疊法﹐這種方法給了我們另一種方式去測得導電率。因為你
用這種方法的時候要將所有導電體接在一起，所以叫做堆疊法。歐伊斯和其他人在 1820 年之
後也提供了類似的方法去討論＂多磁場的環境＂ ＂電子電路＂並且能提供＂電路 OLE 強
度＂，而且只需要用到一些很簡單的儀器就可以完成。
Soon after 1820, Humphry Davy and Peter Barlow in England, and
A-C Becquerel in France, were actively investigating the question of the
decreases in current as the lengths of the conductors in a circuit were
increased, and they also investigated the conductivities of various metals
used as the conductors. In 1825 there was much confusion in the minds and
in the reports of experimenters because of the heritage of electrostatic
concepts. Tension, current, conductivity, resistance, quantity of electricity,
internal resistance of the pile, and many other variables were not clearly
understood or well defined, nor had any units or standards yet been
established. Ohm’s investigations and conclusions were a major advance in
defining essential parameters and understanding the relationships between
them.
到了 1820 年，英格蘭的赫佛利．大尉、 彼特．巴羅 以及法國的 A- C 貝克蘿歐 積極的研究
導體在為什麼當導體的長度增加而電流卻會減少，還有不同導電率的金屬當導體時為何電流會
不一樣。在 1825 年有很多實驗結果讓人家感到很困惑，主要原因是因為他們只有傳統靜電的
觀念，沒有電流的觀念。張力、電流、導電率、電阻、電子數量、電路上每一物體的內電阻和
等等的未知數都沒有被明確的定義或了解，也沒有人建立過類似的單位或是一個標準，而歐姆
的發現和結論就是給了我們這方面的定義：單位和討論之間的關西。
Georg Simon Ohm (1789-1854) (Figure 16.1) was born in Erlangen,
Bavaria, the oldest son of seven children in a Protestant family, with only
two boys and one girl surviving to adulthood. Ohm’s father was a master
locksmith, and his mother was the daughter of a master tailor. The father
was self-taught, but was knowledgeable in mathematics, physics, chemistry,
and the philosophies of Kant and Fichte. The father tutored his sons and
was the most influential part of their education. They each developed
remarkable mathematical talents.
喬治．賽門．歐姆 (1789-1854)出生在巴勒維亞的鄂雷根。歐姆是波特斯登家族七個子女中最
年長的一位，而七位中只有兩個男孩和一個女孩成功的長大。歐姆的爸爸是一個大師級的鎖
匠，他的媽媽是一個女裁縫高手。他爸爸自己學習東西過很多東西，知識非常淵博，他學過數
學、物理、化學還有凱特哲學、法毅地哲學。他的爸爸自己教導他的兒子，這段教育對他們來
說有重要的影響，這讓他們每個人都有過人的數學才能。
The Story of Electrical and Magnetic Measurements
電子儀器和磁學儀器的故事
Figure 16.1 Portrait of Georg Simon Ohm. (Photo courtesy of Deutsches
Museum München.)
圖 16.1 喬治．賽門．歐姆 的肖像(感謝帝奇肆博物館提供圖片)
In growing up, Ohm helped his father machine and repair locks, which
formed the basis of skills he used in later years in designing and building
his experimental equipment and measuring instrumentation. In 1805 be
entered the University of Erlangen. A little over a yew later, because of his
supposed overindulgence in dancing, billiards and ice skating, his stern
father sent him to rural Switzerland, near Bern, where he taught elementary
mathematics. In the spring of 1811, Ohm returned to the University of
Erlangen, and in October he received his PhD degree. After that, he taught
mathematics and physics without salary at Erlangen, followed by several
uninspiring and unimportant positions at lower schools in Bavaria. He
badly wanted to become a university professor of mathematics, and often
felt discouraged by his jack of progress. Many of his activities in the
following years were directed toward achieving his goal of becoming a
professor.
長大之後歐姆打鎖和修鎖，這些能力能為他往後設計實驗器材和建立
測量儀器的基礎
In 1817 Ohm was offered the position of Oberlehrer (senior assistant
master) teaching mathematics and physics at the Jesuit Gynmasium in
Cologne, as a result of his first publication, an elementary geometry text.
The school provided him with a well-equipped physics laboratory, which
excited his interest in experimentation. He then began to study the works of
the French scientists and mathematicians: Lagrange, Legendre, Laplace,
Biot, Poisson, and Fresnel. Oersted’s announcement in 1820, that an
electric current was accompanied by a magnetic field, guided his interests
toward electricity and magnetism, and he began to experiment in these
fields.
As a secondary schoolteacher, Ohm was excellent and well respected.
One of his pupils, Dirichlet, became a great celebrity as a mathematician.
But, after eight years in Cologne, Ohm was again becoming restless and
discouraged. He felt that he was working with too many students who were
not interested in learning, that he had too little free time and few chances of
his ever finding a university professorship. He also began to realize that he
probably would never be married.
In early 1825, still working at the Jesuit Gynmasium, and even
though he was not apart of the scientific community, he began doing
research that he felt would be worthy of ublication, and which he hoped
would gain him the recognition and the professorship he desired. In May
1825 his first scientific paper was published simultaneously in
Schweigger’s Journal fur Chemie und Physik and in Annalen der Physik,
whose editor since 1824 was Johann Poggendorff. The title was
“Vorlaufige
Anziege
des
Gesetzes,
nach
welchem
Metaile
die
Contractelectricitat leiten” (Preliminary Announcement of the Laws,
According to which Metals Conduct Contact Electricity). His objective was
to determine the relationship between the decrease in the electromagnetic
force surrounding a current-carrying wire and the length of the wire, as he
put longer and longer wires into the circuit.
Ohm’s paper was not illustrated, but it gave a verbal description of his
experimental setup. Figure 16.2 is a diagram made from the text. Wires A,
B, and C were called the invariable conductors”; they totaled four Fusse
(feet) long and were one and one-quarter lines thick (one line equals
one-twelfth of an inch). The “variable conductors” completed the circuit;
they were measured one at a time, with one end placed in cup N and the
other in cup O. To measure the magnetic force of the current, Ohm
suspended a magnetized needle over conductor C, following Coulomb’s
earlier examples of torsion balances. It hung on a ribbon torsion element
with a knob on top, graduated in 100 parts. Ohm assumed correctly that the
strength of the magnetic field surrounding the conductor was directly
proportional to the current flowing in the wire.
Figure 16.2 Ohm’s experiment (“hydroelectric circuit”) for determining the
relationship between the length of a wire and electromagnetic
force.
The Story of Electrical and Magnetic Measurements
The electromotive force was provided by a single chemical cell with a
zinc and a copper electrode in a trough 13 inches high and 16 inches long;
the electrolyte was dilute sulfuric acid.
The whole apparatus was oriented m the earth’s magnetic meridian
with the conductor C pointing north and south, so that when the magnetized
needle was made parallel to C, its deflection was not affected by the earth’s
field. The rotation of the knob of the torsion balance required to restore the
needle to its original position, parallel to C, was read in divisions marked
on the torsion head, and the loss of force calculated.
Ohm used six variable conductors: o, a, b, c, d, and e, whose lengths
were I/3, 1, 3, 6, 10 1/3, and 25 feet. With the exception of o, which was
“very thick,” all were 0.3 line in diameter. In Ohm’s next paper, published
a year later in February 1826, he wrote that the wires in these earlier
experiments were made of brass.
Ohm established his normalizing force as that measured when using
conductor o, the very thick wire. He defined his “loss of force” as equal to
the difference between the normal force and the lesser force with the
selected longer wire, divided by the normal force. It is not entirely clear
why Ohm chose the reduction in electromagnetic force as his dependent
variable; but fundamentally, that was the effect he set out to measure.
Tabulating and plotting the results of the six lengths of wire, Ohm
found that his data were well represented by υ = 0.41 log ( l + x ) where υ is
the loss of force and x is the length of the wire in feet. The relationship was
derived by fitting the equation to his data. Ohm included the results of his
measurements and his computed values in his paper, which are given in
Table 16.1.
Ohm also measured a 75-foot-long wire and found that the
experimental value agreed closely with the computed value.
Ohm differentiated his relationship, v = 0.41 log (l + x ), in trying to
obtain a better understanding of the physical meanings of its terms. He
reported
dx
dv = m 1+x
This suggested to him that the general equation might be:
dx
dv = m a+x
where a might depend on length of the fixed conductors, and m was a
function of the normal force, the thickness of a, and the electrical tension of
the force.
If so, the formula becomes
(
dv = m 1＋ ax
TABLE 16.1
)
Reduction in Normalized Electromotive Force vs. Conductor Length
Conductor
o
a
b
C
d
e
Loss of strength, observed
0.00
0.07
0.16
0.24
0.32
0.49
Loss of strength, computed
0.00
0.07
0.16
0.25
0.34
0.50
In making the readings of the torsion balance. Ohm uncovered a curious
fact: when the conductor o was placed in the circuit, the initial magnetic
strength was too great, and he had to wait while it was settling. Using the
other conductors, the initial values were too small, and he had to wait half a
minute for them to reach a reasonably steady value. The experimental setup
was not as stable as Ohm would have preferred.
Three years earlier, in 1822, Thomas Seebeck published his discovery
of thermo-magnetism, which became the basis of thermoelectricity and
thermocouples. Seebeck
investigated many combinations of metals, but frequently used bismuth and
copper.
In 1824 Poddendorff became the editor of Annalen der Physik und
Chemie (what is now Annalen der Physik). In the previous years he had
experienced the instabilities of hydroelectric cells (chemical electric cells)
as they polarized, and appreciated the relative stability of the thermal cells.
In Ohm’s paper published in his journal, Poggendorff added the
editorial footnote: “It would be wished that the author would find the time
to use the so-called thermoelectric circuit to determine these and similar
laws. The operations with it are far more steady than those with the
so-called
hydroelectric
circuit,
and
would
permit
very
exact
measurements.”
The same month that Ohm published his results. May 1825, a review
of the work done by Peter Barlow in England and A-C Becquerel in France
appeared in Ferussac’s “Bulletin des sciences mathematique” in Paris, on
their results in studying electric conduction in different lengths and
thicknesses of wire, and the conductivities of various metals. Humphry
Davy, in England, was also investigating these phenomena. There was not,
however, general agreement in the conclusions reached by Ohm, Barlow,
Becquerel, and Davy. Furthermore, Ohm began to doubt the logarithmic
relationship he had published, if he were to use very long conductors. Ohm
then resolved to repeat his experiments, and to use the thermoelectric
source recommended by Poggendorff.
Ohm published his second major paper in February 1826,
titled:“Bestimmung
des
Gesetzes,
nach
welchem
Metalle
die
Contaktelectricitat leiten, nebst einem Entwurfe zu einer Theorie des
Voltaischen
Apparates
und
des
Schweiggerischen
ultiplicators.”
(Determination of the Law with which Metals Conduct Contact Electricity,
together with the Outline of a Theory of the Voltaic Apparatus and of
Schweigger’s Multiplier). It appeared in Schweigger’s journal.
In the beginning part of the paper, he reported that he had measured, a
year earlier, the
relative conductivities of wires made from a number of metals, using his
hydroelectric cell. All the wires were drawn to be the same diameter. In
comparing the conductivities, Ohm arbitrarily chose copper to be 1,000.
His results indicated that, to have the same conductivity as his copper wire,
the relative lengths of the other conductors were: gold 574, silver 356, zinc
333, brass 280, iron 174, platinum 171, tin 168, and lead 97. This ranking
was again a demonstration that it is an oversimplification to believe that
"metals are conductors and silk is an insulator," and that materials do not
fall neatly into three categories: conductors, semiconductors, and insulators.
Ohm was a mathematician and was used to working with variables that had
a range of values.
Six months after these measurements, in repeating his earlier
experiment. Ohm found that his silver wire was not drawn properly; the
lubricant on the die caused the conductor to be much thinner than he
realized. Silver, he reported, is a much better conductor than copper.
In 1826 metallurgy was another source of errors. Small impurities in
copper, for example, were later shown to decrease its conductivity
substantially.
Ohm also measured wires of different diameters (from 0.12 line to
1.40 lines) and lengths, and independently reached the conclusion that
"cylindrical conductors of the
Figure 16.3 Diagram of Ohm’s thermoelectric circuit: abb'a'－Bismuth strip.
Abcd; a'b'c'd'－Copper strips. Mm'－Mercury cups. vv－Glass
cylinder. nop－Fixed part of torsion head. qrs－Movable part of
torsion head. tt－Magnetic needle with cylindrical ivory caps. uu－
Graduated brass arc. h－Projection-supporting lens. l－Lens of
one inch focal length.
same substance, but different diameter, have the same conductivity values
if their lengths
are in proportion to their cross sections." Barlow and Becquerel had also
reported this
relationship.
The most important part of Ohm's February 1826 paper, however,
was the report of
his constructing a thermoelectric source, as Poggendorff had suggested, and
using it to
measure the relationship between the lengths of his "variable conductors"
and the
resulting magnetic force as longer and longer wires were used. Ohm chose
copper and
bismuth as the two metals of his thermocouple.
Figure 16.4 Reproduction of Ohm's thermoelectric apparatus. (Photo courtesy of Science &
Society icture Library, Science Museum, London.)
Ohm carefully described his experimental apparatus; it is
diagrammed in Figure 16.3, as described in Ohm's paper (a reproduction is
shown in Figure 16.4). In Figure 16.3 the bismuth bracket, abb'a'm was cast;
bb' was six and one-half inches, and ab and a'b' were each three and
one-half inches. The bismuth was nine lines wide and four lines thick
throughout. The copper conductors formed parts of the thermocouples and
ended in the mercury cups; they were nine lines wide and one line thick.
Ohm fastened the bismuth tightly to the copper by using two screws in each
leg.
The magnetic needle, tt, was made of steel wire 0.8 line thick, and
not quite two inches long. Each end was capped by a small ivory turning,
one of which carried a slightly curved fine brass wire that acted as a pointer
above the graduated brass arc, uu.
The needle was suspended from the torsion head by a strip of fine
gold band five inches long. Ohm tested its elastic limit by blocking the
needle from turning. He then rotated the head through more than three
complete turns; upon returning the head to its beginning position, he noted
that the needle remained in its original position when it was unblocked.
Ohm preferred to use ribbon torsion elements rather than the cylindrical
wires that Coulomb had used. A glass tube, w, supports the torsion head
and encloses the moving parts.
Figure 16.5 Heater and cooler for Ohm's thermoelectric apparatus (shown in Figure 16.3): A,
heater; B, cooler, xx, cavities for reception of copper-bismuth junctions; y,
opening for water; zz, outlet for steam.
The cross-section diagrams of the heater and the cooler for the two
legs of the thermocouples are in Figure 16.5. The containers, A and B, were
made of tin A the heater, contained boiling water, had a small flame to keep
the water boiling, and a vent pipe for discharging steam. It also had an inlet
for pouring in more water, which could be closed by a cork to lessen the
heat loss. B, the cooler, was packed with moistened ice or snow readily
available in January when the measurements were made.
The two thermocouple legs, ab and a'b', were carefully wound with
several turns of closely woven silk cloth, to insulate them electrically. The
wells xx in the heater and cooler were deep enough to accommodate about
one inch of small lead shot under the two thermocouple legs, and to provide
heating and cooling to practically the fall area where the bismuth and
copper were on contact with each other. After the two legs were inserted
into the heating and cooling cavities, the remaining space was filled with
bits of glass.
Ohm prepared eight different conductors to be measured, denoted 1,
2, 3, 4, 5, 6, 7, 8, whose lengths were 2, 4, 6, 10, 18, 34, 66, and 130 inches.
They were all made from a “plated copper” wire seven-eighths line thick.
In this experiment Ohm recorded the divisions of rotation of the torsion
knob required to return the needle to its original position, and used this
measurement in his analyses. He did not use the fractional relationship he
had used in his previous paper. Ohm, again, oriented his apparatus so that
the conductor carrying the current being sensed was in the magnetic
meridian.
Analyzing the results from his measurements of the wires, Ohm
concluded that the relationship between the restoring torque and the length
of the conductor can be very satisfactorily expressed by the equation
a
x = b+x
TABLE 16.2 Division of Restoring Torque vs. Conductor Length
Conductor#
1
3
5
7
8
X, measured
305 1/2
259
177 3/4
79
45
X, computed
306
259
178
79
45
where X is the strength of the magnetic effect on the needle measured in
divisions of the torsion knob, x is the length, in inches, of the conductor
being measured, and a and b are constants. If the value of b is 20.25, and a
is 6800, the measured and computed values agree very well. Table 16.2
gives the values for several of the conductors.
Ohm next remeasured the relationship X = a/(b +x) using a smaller
temperature difference between the two couples. He let the warm end of the
thermocouple pair come to room temperature, 7.5 degrees Reamur (9.4
degrees Celsius, 48.9 fahrenheit,—the experiment was performed in
January), and he kept the cold junction again at 0 degrees Reamur and
Celsius with ice. He measured the same eight wires he had previously used,
when the thermocouple ends were at boiling and freezing temperatures, and
reported that b was again 20.25 and this time a was 617.
Ohm drew several conclusions from these results. First, the equation X
= a/(b + x) was valid for two very different values of the exciting force, and
was probably true for all values. Also, b remains the same even though the
exciting force is reduced by more than a factor of 10. Thus, b is dependent
simply on the unchanged part of the conducting circuit, and a is dependent
simply on the exciting force. Second, it appeared that the force in the
thermoelectric circuit was almost exactly proportional to the temperature
difference between the two thermocouples. One of Ohm's great talents was
his ability to represent the results of his experiments mathematically and to
relate the terms of his expressions to the physical realities of what he was
measuring. He was also comfortable in working back and forth between the
measured data and the mathematical expressions.
Ohm also confirmed Davy's findings that the conductivity of a metal
varied with its temperature. By measuring a brass wire four inches long at
room temperature, it produced 159 divisions. When he heated the wire in
the middle with a spirit lamp, the force fell off by 20 or more divisions, and
did not change when he moved the flame to one end or the other. When
Ohm placed a lump of solidified snow around the wire, the force increased
by two divisions. He commented that these observed changes should
caution experimenters that varying ambient temperatures can cause small
irregularities when they are making conductivity measurements.
In comparing his thermoelectric to his hydroelectric source. Ohm
reported that the exciting force, a, is far greater in the hydroelectric source.
The value of b, with the thermoelectric source, is less than one hundredth
the value of the hydroelectric source. Also, in the hydroelectric, the strength
of the current affects both a and b, because of changes in the electrolyte
which he did not understand. With the thermoelectric source, however,
when the difference in temperature between the two couples is constant,
both a and b are constant.
Ohm appreciated the stability which the thermoelectric source
provided, and reported that he had observed, when measuring the
two-inch-long conductor between the mercury cups, there was no change in
the reading during the period between the initial deflection and the
deflection one-half hour later. A year earlier, using the hydroelectric cell
and the “very thick” unknown, he recorded that his initial deflection was
180 divisions, and fell slowly to 111.75 divisions a half hour later.
At the close of his paper. Ohm reported that by understanding that
the exciting force of a hydroelectric cell is far greater than that of a
thermoelectric cell, it explained the anomaly that while both sources could
produce electromagnetic action, the hydroelectric cell could produce
electrochemical reactions which the thermoelectric cell could not do.
Ohm also observed that his equation X = a/(b + x) explained many
phenomena which had heretofore been mysteries in understanding the
results of Poggendorff, Nobili, and other experimenters. When Poggendorff
was an undergraduate and measured his sets of 100-tum coils, using a
hydroelectric cell (published in "Isis" in 1821), he reported three
observations:
‧ That there is a maximum effect for the multiplier, which cannot be
exceeded
‧ This maximum remains the same for pairs of large or small plates
of the pile, but
the number of turns on the multiplier required to produce it
depends on the size of
the plates, and is, moreover, larger in the case of the smaller
plates
‧ That the multiplier made out of thick wire gives the greater
maximum of effect
Ohm could not reduce Poggendorff’s results to numerical
relationships because the essential data were lacking. But to confirm
Poggendorff’s results and his own formula, he made two coil multipliers,
each with 220 turns, and about two inches in diameter. One was made of
wire one-fifth line thick, the other used one-twentieth line thick wire. Using
the
same-sized
copper-zinc
cell
as
Poggendorff
used,
with
3
1/4-inch-diameter plates, the thick-wire one gave 263 divisions deflection
of a compass needle in the center of a coil, and the thin-wire one only 68
divisions, indicating that the thicker wire gave a much stronger effect,
because the stronger current flows through the thicker wire.
Ohm commented farther that when using a multitum coil with a
thermoelectric circuit, the resistance of the wire of the coil increases the
resistance of the circuit more rapidly than it increases the strength of the
magnetic field. He wrote that Nobili, when using such a source, derived the
sensitivity of his galvanometer more from the magnetic strength of his
needles and their delicate suspension than from the many turns of the coil
driving the indicating needles. When Ohm used a compass and a 60-tum
multiplier of one-fifth line wire, warming a couple in his hand gave a
needle deflection of about 20 degrees. When he used a single turn, the
deflection always exceeded 70 degrees.
In April 1826, two months following his previous paper, Ohm
published an extension of his ideas: “Versuch einer Theorie der durch
galvanische Krafte hervorgebrachten elektroskopischen Erscheinungen”
(Investigation of a Theory according to which Galvanic Actions Produce
Electroscopic Phenomena). It was a short paper, which appeared in
Poggendorff’s Annalen. The themes were abstract and theoretical, dealing
with electric tensions and conductibility. In developing his ideas and
equations, Ohm put all the resistances of the circuit into one term, and
stated his law in the form we use today, X=a/l, I = V/R.
After his last three publications. Ohm began to feel that his new
understandings should appear in a book, and he applied for a year's leave of
absence from the Jesuit Gymnasium so that he could have sufficient time
for writing. The leave was granted in the summer of 1826; Ohm was to
receive one-half of his previous salary. He moved to Berlin, which had
much better libraries and greater scientific activity. Also, his younger
brother, Martin, was living in Berlin.
A year later, in 1827, Ohm's book, “Die galvanische Kette,
mathematisch bearbitet” (The Galvanic Circuit Developed Mathematically),
was published in Berlin. It was his major work. Ohm was familiar with
Fourier's “The Analytical Theory of Heat,” which was published in 1822,
and he believed that the flow of electricity from higher tensions to lower
ones was analogous to the flow of heat from high temperatures to lower
temperatures, and that the electric currents and the heat flows depended on
the conductivities of the metals through which they were passing. Ohm
patterned his book on Fourier's “Theorie...,” which had no experimental
data and was written in abstract style with much mathematics. He credited
both Fourier and Poisson in his book. Ohm was probably unaware of
Fourier’s difficulties in having his 1807 monograph and his Prize Paper
published, and Ohm also
AF, CD and BG are proportional to electrical potentials at points
A, C, and B along conductor AB (BG + GH = AF)
Figure 16.6 A simplified example of Ohm’ original illustration of the fall of
electrical potential in a conduct of length AB.
must have greatly overestimated the number of people who had read and
understood his earlier papers.
Ohm based “Die galvanische Kette...” on his previous experimental
work and data, and divided it into three sections: Introduction, The Voltaic
Circuit, and Appendix. In the introduction, intended for those readers not
completely familiar with mathematics, he used graphical presentations to
convey his ideas. Figure 16.6, an example simplified from the original,
illustrates the fall of potential, or tension, as the current flows through a
circuit laid out as a line rather than a loop or a ring. AB represents the
circuit; the lines AF and BG, perpendicular to AB, indicate by their lengths
the force of the electricities at the extremities A and B. Quoting Francis'
translation: “If now the straight line FG be drawn from F to G, also FH,
parallel to AB, the position of FG will give the mode of separation of the
electricity [in today's language: the difference of potential existing between
the extremities or the total electromotive force at work in the circuit], and
the quantities BG, -AF or GH the tensions occurring at the extremities of
the ring; and the force of the electricity at any other place C, may easily be
expressed by the length of CD drawn through C perpendicularly to AB...”
Ohm then developed his presentation to illustrate circuits composed of any
number of sections of varying conductor sizes and materials.
The Voltaic Circuit part consisted of discussions of observations and
derivations:
‧ Current is of equal strength in all parts of
‧ Development of S= A/L (X = a/l)
‧ Conductors in series and parallel
‧ Distinctions between thermo-and hydro-electric circuits
‧ Greater electromotive force and resistance of a battery depends on
the number of
elements in series
‧ Action of a galvanometer
‧ Decomposing power of a current
The Appendix, “On the Chemical Power of the Galvanic Circuit,” was
a discussion of circuits causing chemical changes.
The scientific community scarcely noticed Ohm’s book, and it was
very slow in being appreciated. One or two exceptions were scientists who
took advantage of its insights, and another few who denounced the work.
Very few copies had been printed, which also limited its readership. It was
reviewed only once, in the Berlin “Jahrbucher fur wissensch-after Kritik”
(Yearbooks for Scientific Criticism) by Georg Friedrich Pohl, professor of
physics at the Friedrich Wilhelm Gymnasium in Berlin. Pohl reported that
Ohm's book was theoretical and hypothetical, with no basis of fact.
In addition, in 1827, the terms for describing current electricity were
not well defined, universally agreed upon nor widely used. Besides, most
scientists found Ohm's text very difficult to read and understand; and there
were other little-known authors writing on the same subject. Ohm's
previous papers, which contained much experimental data, had not been
widely read, though they had appeared in respected journals. Also, Ohm's
choice of an abstract presentation of his ideas in his book made it difficult
to associate with everyday experimentation.
By March 1828, Ohm had decided that he did not want to return to
Cologne, and resigned from the Gymnasium there. Soon afterward he
applied to the Prussian Ministry of Education for a position, enclosing a
copy of his resignation from the Cologne gynasium and a copy of his “Die
galvanische Kette.” He was hoping for a university professorship, but was
offered a position at the Allgemeine Kriegsschule (General War School) in
Berlin teaching mathematics three days a week. He was very disappointed,
but accepted the offer. In 1832 he taught classes at the Vereinigte Artillerie
und Ingenieurschule (United Artillery and Engineer School) also in Berlin.
A turning point came in October 1833; Ohm joined the Polytechnische
Schule in Nuremberg in Bavaria as a professor of physics. It was not a
university appointment, but it carried the title of professor and was the
beginning of the recognition that Ohm desired.
In 1839, Claude Pouillet in Paris published his confirmation of Ohm's
results. He measured weak currents with his tangent and sine
galvanometers, and improved Ohm's accuracy. For years, though, in France,
Pouillet was credited for developing Ohm's Law, rather than improving its
accuracy.
Also in 1839, Ohm was elected a Corresponding Member of the Berlin
Academy. In 1841 he became a Corresponding Member of the Turin
Academy in Italy.
In England, Wheatstone, involved in telegraphy, recognized the value
of Ohm's work. He repeated some of Ohm's experiments and published the
results. In 1841 Ohm was appointed a foreign member of the Royal Society,
an honor previously received by only one other in Germany, Gauss.
In 1849 Ohm was called to be the curator of the physical cabinet at the
Bavarian Academy in Munich, which later became a part of the Deutsches
Museum. His new position carried an obligation to lecture at the University
of Munich as a fall professor. Then, in 1852, Ohm received the chair of
physics at the University of Munich, fulfilling his lifelong ambition. Less
than two years later, in October 1854, he died.
Sources and Recommended Reading
Florian Cajori: A History of Physics, The Macmillan Company, New York,
1899 and 1933.
Dictionary of Scientific Biography:
Kenneth L. Caneva: “Ohm,” Vol. 10
Jerome R. Ravetz and I. Grattan-Guinness: “Fourier,” Charles Scribner's Sons,
New York, Vol. 5,
pp. 93-99,1972-1974.
M. S. Gupta: “Georg Simon Ohm and Ohm's Law,” IEEE Transactions on
Education, Vol. E-3, No.
3, August 1980.
N. H. de Vaudrey Heathcote: “A Translation of the Paper in Which Ohm First
Announced His Law
of the Galvanic Circuit, Prefaced by some Account of the Work of His
Predecessors,” Science Progress, Vol. 26, No. 101, pp. 51-75, July 1931. The
original paper, titled “Bestimmung des Gesetzes, nach welchem Metalle die
Contactelekricitat leiten, nebst einem Enrwufe zu einer
Theonedes Voltaischen Apparates und des Schweiggerschen Multiplactors,”
waspublished in Schweigger’s, Joumalfur Chemie und Physik, Vol. 46, pp.
137-166, 1826.
Klemm, Teichmann, Hermann, Auer: “150 Jahre Ohmsche Gesetzes,”
Sonderdruck, Electrotechnische Zeitschrift, Ausgabe a, Bd. 98, H.1, S.94-102, H.2, S.158-160,
VDE-Verlag GmbH, 1000 Berlin 12, 1977.
Dr. G. S. Ohm: The Galvanic Circuit Investigated Mathematically, Berlin, 1827.
Translated by William Francis, with a Preface by Thomas D. Lockwood,
M.I.E.E. D. Van Nostrand Company, New York 1891 Kraus Reprint Co.,
New York, 1969.
Dr. G. S. Ohm: “Versuch einer Theorie der durch galvanische Krahe
hervorgebrachten elektrosko- pischen Erscheinungen,” Poggendorff’s Annalen
der Physik und Chemie, Vol. 6, pp. 459-469, and continued in Vol. 7, pp.
45-54 and 117-118, 1826.
Dr. G. S. Ohm: “Vorlauhge Anzeige der Gesetzes, nach welchem Metalle die
Contaktelektricitat leiten”, Schweigger’s Journal fur Chemie und Physik, Vol.
44, pp. 110-118, 1825.
Poggendorff’s Annalen der Physik und Chemie, Vol. 4, pp. 79-88, 1825.
F. S. Shoucair: Volta,Ampere,Ohm, and Kirchoff: Electrical Engineering’s
Forgotten Immortals, Brown University, Providence, RI, 1985.
Dr. Jurgen Teichmann: “Begriff, Experiment und Vorurteil-derlange Weg zum
Ohmschen Gesetz,” Naturwissenschaften im Unterricht-Physik/Chemie, N. 50,
1989.
Dr. Jurgen Teichmaan: 150 Jahre Ohmsches Gesetz, 1826 is 1976, Festschrift
Deutsches Museum, Munchen, 1976. Sonderdruck, Elektrotechnische
Zeitschrift, Ausgabe a, Bd. 97, H. 10, S. 594- 600, VDE-Verlag GmbH, 1000
Berlin12, 1976.