The Edison Dynamo and the Parallel Circuit
Perhaps in no other case has the relationship of science to engineering been more significantly misunderstood than in the work of Thomas Edison. Edison continues to be remembered as an inventor who is thought to have merely applied scientific discoveries made by others. In fact, Edison understood the implications of Ohm’s and Joule’s Laws in a way that eluded some of the leading scientists and theoretically-minded engineers of his time, who believed that the subdivision of electricity for light was fundamentally impossible.
The error on the part of these experts was not faulty scientific logic but sound reasoning—based on narrow assumptions of a kind that are often typical of professional groups when judging new ideas in terms of their dated frames of reference. An example of such thinking, cited in a seminal 1951 article by Harold Passer, occurred in an 1879 book on electric lighting by the British specialist Paget Higgs, who concluded—on the eve of Edison’s great breakthrough—that a parallel circuit for distributing electricity to a network of lights could not possibly work.1 Higgs used detailed calculations based on the latest scientific understanding. The key calculations are as follows:
For a constant voltage, Higgs showed that the maximum power output in an electric circuit consisting of a power source, a line, and lamps occurs when the resistance in the lamps (R2) is equal to the sum of the resistance in the power source and the resistance in the line (R1). This equation held with a battery circuit and engineers trying to apply science believed that dynamos had to be designed with R2 equal to R1.
For a given voltage V, and R2 = α R1, the total resistance R1 + R2 will be R1 (1 + α), and the current I will be V / R1 (1 + α). The power in the lamps will then be:
The maximum power in R2 will be found when the derivative of α / (1 + α)2 equals zero:
from which 1 + 2α + α2 - 2α - 2α2 = 1 - α2 = 0, so that α2 = 1, or α = 1, from which R2 = αR1 = R1.
From this mathematically correct result, Higgs argued that for a series circuit with n lamps, and a constant power source (W1) to run the dynamo, the heat in the lamps (H) would be:
He argued next that since the total light varies inversely as n, the light emitted (L1) in the series circuit would be:
By the same reasoning, for a parallel circuit with n lamps, the total resistance of the lamps would be R2/n and thus:
He then assumed that, for the series circuit, R1 is so small compared to nR2 that it can be taken as zero, so that L1 = W1/n, whereas for the parallel circuit he assumed that R2/n will be so small compared to R1 that it can be neglected in the denominator, leading to the result:
These results were for the networks. Higgs divided each network by n to get the light for each lamp, which was proportional to 1/n2 for the series circuit and 1/n3 for the parallel one. He concluded that subdividing the current in a parallel circuit was “hopeless.”2
Higgs, and other experts at the time, made the fundamental error of assuming that the mathematical proof for R1 = R2 was a reasonable proof for design. As Edison had recognized, it was not. Higgs’s result showed the maximum power output, but it did so at a disastrously low efficiency. This can be easily shown for the case where R1 = 10 ohms and R2 = 10 ohms, when compared to the case where R1 = 10 ohms and R2 = 90 ohms.
In both cases, if V = 100 volts, then in the first case the current I = 100/20 = 5 amps. The dynamo power P = VI will be 100 (5) or 500 watts and the power output to the lamps P = I2R will be 52 (10) or 250 watts, an efficiency of only 50 percent. In the second case, I = 100/100 = 1 amp. The dynamo power P =VI will be 100 (1) or 100 watts and the power output to the lamps P = I2R will be 12 (90) or 90 watts, an efficiency of 90 percent. From these relationships Edison recognized the need to reduce resistance in the dynamo and to use a high resistance lamp.
The flaw in Higgs’s thinking lay not in his science—he used Ohm’s and Joule’s Laws correctly—but in his assumption that the engineer should use scientific laws as the basis of design, rather than as guidelines within which to make choices. In engineering, it is only after the designer sees the way to make a true innovation—one that is both efficient and economical—that the equations become useful and essential.
1 Harold C. Passer, “Electrical Science and the Early Development of the Electrical Manufacturing Industry in the United States,” Annals of Science [London], vol. 7, no. 4 (December 28, 1951), pp. 382–92; and Paget Higgs, The Electric Light (London, 1879), pp. 158–75.
2 Paget Higgs, The Electric Light, p. 174.