Popular Science Monthly
��465
��this, or 0.000373 henry. One micro- farad is one-milHonth of a farad ; hence the capacity in farads is one-milHonth of 0.0012 microfarad, or 0.0000000012 fa- rad. Taking up the rule for compuHng the time period, the first step is to mul- tiply the capacity in farads by the in- ductance in henrvs (0.0000000012 times 0.000373 = O.OOOObOOOOOOO-147 ) . The sec- ond step is to take the square root of this number, which is found to be 0.000000669. The third step is to mul- tiply this by 6.28, which gives 0.0000042 second as the time period. Thus it ap- pears that the alternating current passes through a complete cycle in only 42 ten- millionths of one second, and that the frequency (which is the reciprocal of this) is a little over 236,000 cycles per second. This agrees with the result se- cured from the first calculation above.
If several other sets of capacity and inductance values
are worked out by i r
both the above J
rules, the same agreement will be found. It thus be- comes clear that ^'^- ^- ^^"P'^^ the resonant fre- quency at which any conden .e* -circuit will oscillate most strongly, i^ practi- cally identical with the frequency of the free alternating current which will be produced if that circuit is ^tt into vibra- tion by a sudden discharge within itself. Referring to Fig. 1, if the capacity of the antenna is charged by a gradually rising voltage supplied from the secondary of a transformer through terminals T, T, a j)oint will be reached beyond which no energy can be forced in, because the air between the spark-balls at 6" will break down. The spark which then occurs completes the oscillating circuit from the earth E through the inductance L to the antenna A, and the stored electrical en- ergy rushes to the ground. By the over- shooting action which alwa)'s takes place, if the circuit resistance is not too great, the current surges back and forth. The frequency of the alternations thus pro- duced is that which may be computed as in the paragraph above. This frequency is practically the same as that which would produce the greatest current in the antemia, if the transfomier were dis-
���connected and the spark-gap replaced by a '^igh-frequency alternator in such a way that the total inductance and ca- pacity remained the same.
An entirely similar condition exists for the closed circuit of Fig. 2. Here a con- denser C, a spark-gap S, an inductance L and a resistance R are connected in series. The terminals of a high voltage transformer, to charge the condenser, are connected at T, T. If the potential applied across the condenser is gradually increased, a charge will be stored in it by virtue of its electrical capacity. When the voltage becomes so high that the spark-gap breaks down and a spark passes, the con- denser discharges through the induc- tance and resis- tance. If the re- sistance is not too high, the discharge will be oscillatory, and the frequency of the oscillations (and their time - period)canbecalcu- "lated according to the three steps of the same rule given for antennas. Thus the number of cycles per second of the free alternat- ing-current discharge in the circuit can be found, if its inductance and capacity are known. The wavelength which would be set up by currents of this fre- quency may also be determined easily, as has been shown.
If the transformer is disconnected and a high-frequency alternator substituted for the spark-gap, the circuit will have in it forced alternating currents of the frequency at which the alternator gene- rates. As was shown in January, the greatest current will flow when the fre- quency of minimum impedance (or zero reactance) is reached. This is the re- sonant frequency and has practically the .same numerical value as that of the free oscillations discussed in the paragraph immediately preceding.
The foregoing descriptions should give a clear indication of the difference between free and forced alternating cur- rents in oscillation-circuits. If a sus- tained, alternating voltage is applied to
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