Page:Popular Science Monthly Volume 63.djvu/198

194 Very great care is required in the insulation of the secondary circuit of an induction coil to be used in Hertzian wave telegraphy, because the secondary circuit is then subjected to impulsive electromotive forces lasting for a short time, having a much higher electromotive force than that which the coil itself normally produces.

The primary circuit of a ten-inch coil generally consists of a length of 300 or 400 feet of thick insulated copper wire. In such a coil the secondary circuit would require about ten miles of No. 34 H.C. copper wire, making 50,000 turns round the core. It would have a resistance at ordinary temperatures of 6,600 ohms, and an inductance of 460 henrys. The primary circuit, if formed of 360 turns of No. 12 H.C. copper wire, would have a resistance of 0.36 of an ohm, and an inductance of 0.02 of a henry.

An important matter in connection with an induction coil to be used for wireless telegraphy is the resistance of the secondary circuit. The purpose for which we employ the coil is to charge a condenser of some kind. If a constant electromotive force (V) is applied to the terminals of a condenser having a capacity C, then the difference of potential (v) of the terminals of the condenser at any time that the contact is made is given by the expression:

In the above equation, the letter e stands for the number 2.71828, the base of the Napierian logarithms, and R is the resistance in series with the condenser, of which the capacity is C, to which the electromotive force is applied. This equation can easily be deduced from first principles, and it shows that the potential difference v of the terminals of the condenser does not instantly attain a value equal to the impressed electromotive force V but rises up gradually. Thus, for instance, suppose that a condenser of one microfarad is being charged through a resistance of one megohm by an impressed voltage of 100 volts, the equation shows that at the end of the first second after contact, the terminal potential difference of the condenser will be only 63 volts, at the end of the second second, 86 volts, and so on.

Since e-10 an exceedingly small number, it follows that in ten seconds the condenser would be practically charged with a voltage equal to 100 volts. The product CR in the above equation is called the