Induction-Coil Potentials Page 565

LXV. Induction-Coil Potentials.

By E. Taylor Jones, D.Sc., Professor of Physics in the University College of North Wales, Bangor¹.

[Plate VIII.]

The present paper contains some further applications of the theory of electrical oscillations in coupled circuits, and is a continuation of two former papers² on the subject.

In the first of these it was shown that if a given current is interrupted in the primary of two coupled oscillatory circuits, the potential-difference, \(V_2\), at the terminals of the secondary at any subsequent time \(t\) is theoretically given by an expression of the form

\[ A_1 e^{-k_1 t} \sin(2\pi n_1 t - \delta_1) - A_2 e^{-k_2 t} \sin(2\pi n_2 t - \delta_2), \quad \dots \ (1) \]

where \(n_1\), \(n_2\) are the frequencies of the two oscillations of the system, and the other six constants can be calculated from the capacities, inductances, and resistances of the circuits. This result was illustrated by a number of examples in which coupled air-core coils connected to condensers were used. The wave of potential represented by (1) was worked out for each case and compared with the experimental curve obtained with an electrostatic oscillograph.

In the second paper referred to, the expression (1) was further illustrated by experiments with an ordinary induction-coil with iron core, a number of cases being worked out in some of which the secondary coil, as well as the primary, was connected to a condenser. In these experiments, however, the primary (paraffin-paper) condenser was of considerably greater capacity than that generally used with an induction-coil.

Recently an expression of the form (1) has been given in an important paper by Dibbern³ for the potential-difference at the plates of the primary condenser, and the theoretical curves of both primary and secondary potential compared with the experimental curves obtained with a pendulum interruptor. In his experiments Dibbern used coils with air-cores, cores of iron-filings in paraffin-wax, of iron wire, and of solid iron. Good agreement was found between the

¹ Communicated by the Author.
² “Electrical Oscillations in Coupled Circuits,” E. T. Jones, Phil. Mag. xvii. p. 28 (1909); “The Induction-Coil,” E. T. Jones and D. E. Roberts, Phil. Mag. xxii. p. 706 (1911). These two papers will be referred to as l. c. (1) and l. c. (2).
³ E. Dibbern, Ann. d. Physik, xl. 4, p. 935 (1913); Inaug.-Diss., Kiel.