Nikola Tesla Articles
Induction-Coil Potentials Page 575
Philosophical Magazine - April 1st, 1914
\(V_1\) is the difference of potential at the terminals of the primary condenser which, for the reasons stated above, was connected directly across the primary coil.
The expression for \(V_2\) was accordingly worked out afresh for these new initial conditions, and the results show that the values of \(\delta_1\) and \(\delta_2\) are considerably modified by the change in the conditions. The expressions arrived at are
\[ \tan\delta_1 = 2\pi n_1\left\{2\beta \cdot \frac{n_1^2 + n_2^2}{n_2^2 - n_1^2} - (\theta_1 - 2\theta_0 - \theta_2)\right\}, \]
\[ \tan\delta_2 = \frac{n_2}{n_1} \cdot \tan\delta_1. \]
These reduce to the expressions used in the former papers if \(\theta_1\) is made equal to \(\theta_0\), i.e. \(R_1\) to \(R_0\).
In arriving at the above expressions the squares and product of \(\theta_1\), \(\theta_2\) are neglected. The fuller expressions for \(\tan\delta_1\), \(\tan\delta_2\), including these second order terms, were also, however, worked out for each of the three cases, and found to give values not differing greatly from those calculated from the above formulæ. The difference in \(\delta_1\) was in each case quite negligible, and in \(\delta_2\) less than 1° except in Case II., where it amounted to 2°·5. The values of \(\delta_1\), \(\delta_2\) given in Table V. are those given by the more exact formulæ. This table contains the values of the eight constants of the formula (1) for each of the three cases, the amplitudes being given in volts for \(i_0 = 10\) amperes.
Table V.
| \(n_1\). | \(n_2\). | \(A_1\). | \(A_2\). | \(k_1\). | \(k_2\). | \(\delta_1\). | \(\delta_2\). | |
|---|---|---|---|---|---|---|---|---|
| Case I. …… | 194·3 | 1063 | 258000 | 49420 | 58 | 728 | −3°·5 | −17°·7 |
| Case II. …… | 232·8 | 1102 | 314600 | 75270 | 120 | 1130 | −7°·1 | −28°·8 |
| Case III. … | 304·4 | 1224 | 416500 | 105400 | 96·5 | 1210 | −3°·03 | −11°·4 |
Values of the secondary potential were calculated from these by (1) for various values of \(t\), squared (for comparison with the photographic curves), and plotted over one period of the slower oscillation. The curves are shown in figs. 1, 2, and 3, the maximum potentials indicated being in the three cases 238700, 291400, and 419000 volts respectively.
