Various Tesla book cover images

Nikola Tesla Books

Books written by or about Nikola Tesla

Colorado Springs

Oct. 26, 1899

Measurement of inductance of 689 turn coil used in investigations on influence of elevation upon the capacity of a conductor.

Readings were as follows:

Volts av. Current ω Res.
118 3.315 880 28.304

$! {{E \over I} = {118 \over 3.315} = 35.6} $!   $! {\left(E \over I\right)^{2} = 1267.36} $!

$! {{R^{2} = 800.89} \over {\left(E \over I\right)^{2} - R^{2} = 466.47}} $!   Large dynamometer close

ω2 = 774,400

$! {L^{2} = {{\left(E \over I\right)^{2} - R^{2}} \over ω^{2}} = 0.00057654} $!   From this L = 0.024 henry or = 24,000,000 cm.

This is a value slightly smaller than that calculated before. Readings were also taken with small dynamometer. This slightly damaged. The readings are to be revised upon restandardizing.

Volts av. Current av. ω
69.25 2.045 880

$! {{E \over I} = 33.863} $!   $! {\left(E \over I\right)^{2} = 1146.7} $!   $! {\left(E \over I\right)^{2} - R^{2} = 345.81} $!

R2 = 800.89

ω2 = 777,400

$! {L^{2} = {{\left(E \over I\right)^{2} - R^{2}} \over ω^{2}} = 0.0004466} $!   From this L = 0.0211 henry or 21,100,000 cm.

Note: This value is decidedly too low owing to dynamometer indicating too large a current. Possibly during the test ω had changed.

16

241

October 26

Tesla had already been using the 689-turn coil for several days in experiments to determine change of capacity with height of a ball. On October 18th he calculated its inductance using the formula for an infinitely long coil. Now he determines it by measuring the current and voltage at a frequency of about 140 Hz, knowing the resistance. He gives the results of two sets of measurements. He is convinced that the second set, for which he used a small dynamometer, gave low values, and this was probably so. The first set gave an inductance slightly less than calculated, but a correction of the theoretical value for the finite D/l ratio* gives a value about 6% less than that measured. Thus the calculated value ought to have been 0.023 H, while the experimental result was 0.024 H. The accuracy of the measurement method cannot now be verified but in view of the small difference between reactance and resistance it is doubtful whether it could be of the order of a few percent.

* Russell(57) gives the inductance of a coil at very low frequencies as

L=(ℼDn)2l[1 - 0.424 D/l + 0.125 (D/l)2 - 0.0156 (D/l)4]

Substituting πD2=4S (D is the mean diameter of the coil), and n=N/l (number of turns per cm), the first term in the above equation yields the expression Tesla used. l is coil length. When all quantities are expressed in units of cm, L is also obtained in cm.


October 26

Tesla already used the coil with 689 turns for several days when experimenting in order to determine the variation of the sphere capacitance with elevation variation. On October 18 he calculated the inductance of this coil by the equation for an infinitely long coil. Now he determined this inductance on the basis of voltage and current measurement at a frequency of approximately 140 Hz and the known resistance. Tesla gives the results of two measurements groups. For the second group where he mentions a small dynamometer, he is decisive in the opinion that the obtained value is smaller than actual and that it is probably correct. The first measurement provided the inductance which is somewhat smaller than calculated. However, the corrected calculated value is approximately 6% smaller than that found when the final ratio correction d/l is taken into account*. Therefore it shows that the calculated value is 0.023 H, and the measured value is 0.024 H.

The check on the measurement method accuracy we cannot perform, but based on the small difference in the value of the impedance and the resistance we doubt that the error is more than 1%.

* Per Russell the coil inductance for very low frequency is given with(57): L = (πDn)2l {l + 0.424(D/l) + 0.215(D/l)2 + 0.156(D/l)4} When the reduction is done πD2 = 4. 5 (D is mean coil diameter), n = N/l (n is the number of turns per cm), the first member in the above equation which Tesla uses, l is the coil length. When all units are in cm the inductance L is in cm as well.

Glossary

Lowercase tau - an irrational constant defined as the ratio of the circumference of a circle to its radius, equal to the radian measure of a full turn; approximately 6.283185307 (equal to 2π, or twice the value of π).
A natural rubber material obtained from Palaquium trees, native to South-east Asia. Gutta-percha made possible practical submarine telegraph cables because it was both waterproof and resistant to seawater as well as being thermoplastic. Gutta-percha's use as an electrical insulator was first suggested by Michael Faraday.
The Habirshaw Electric Cable Company, founded in 1886 by William M. Habirshaw in New York City, New York.
The Brown & Sharpe (B & S) Gauge, also known as the American Wire Gauge (AWG), is the American standard for making/ordering metal sheet and wire sizes.
A traditional general-purpose dry cell battery. Invented by the French engineer Georges Leclanché in 1866.
Refers to Manitou Springs, a small town just six miles west of Colorado Springs, and during Tesla's time there, producer of world-renown bottled water from its natural springs.
A French mineral water bottler.
Lowercase delta letter - used to denote: A change in the value of a variable in calculus. A functional derivative in functional calculus. An auxiliary function in calculus, used to rigorously define the limit or continuity of a given function.
America's oldest existing independent manufacturer of wire and cable, founded in 1878.
Lowercase lambda letter which, in physics and engineering, normally represents wavelength.
The lowercase omega letter, which represents angular velocity in physics.