  # Relative Advantagesof Series and Parallel Resonance

(Reproduced from "Zero to Eighty" pp.321-322 by EF Northrup)

Since capacitors are necessary to satisfactory operation of the electric gun, the next problem is to determine in what manner the capacitors are to be connected. There are two general methods of connecting capacitors to produce resonance: series and parallel. Using simplified circuits consisting of an inductance, a capacitor, and a source of electromotive force, we find that in the series resonated circuit the inductor, the capacitor, and the source of e.m.f. all carry the same current. An ammeter inserted in any part of this circuit will indicate the current for all parts of it. In the parallel resonated circuit, the capacitor is connected in parallel, or shunt, across the terminals of the inductor. For convenience, the source of e.m.f. is also considered to be connected across the terminals of the capacitor and inductor. In the parallel resonated circuit, each element of the circuit will generally carry more or less widely differing amounts of the current, which must be separately measured or calculated for each element.

In many circuits, parallel resonance is the accepted method. By means of parallel resonance, enormous currents can be built up between the inductor and capacitor without carrying them through the source of e.m.f. Moreover, in this circuit, resonance does not need to be perfect to maintain reasonably stable conditions of current. In the series resonated circuit, resonance must be very close, or else the current drops off rapidly. As pointed out above, the source of e.m.f. must carry whatever current exists in the circuit. In general, parallel resonance is best adapted to circuits employing high currents at comparatively low voltages, whereas series resonance is suitable where high voltages and small currents are desirable.

At first thought it might seem that parallel resonance is the better method for the electric gun. However, although it appears simple in application, there are serious difficulties which greatly hinder the best operation of the electric gun when the parallel method is used. For instance, if each unit phase coil of the gun is separately resonated either with or without the projectile being in the coil, we have a large number of places where currents due to magnetic induction can flow. Since the coils are coaxial and quite close together, the coupling factor or coefficient of magnetic induction between coils is very high. From experience, it has been found that these induced currents and magnetic induction effects interfere with the action of the polyphase currents in the coils, and tend to diminish the thrust on the projectile.

To minimize these harmful induction effects, series resonance may be used. Although the generator must carry a high value of current, the voltage of the machine need only be high enough to overcome the equivalent resistance of the connected circuit. This is possible, since in series resonance the e.m-f.’s necessary to overcome the reactance of the capacitor and inductor are one hundred and eighty electrical degrees out of phase, and hence neutralize each other.

If the capacity is so adjusted as to cause resonance to occur only while the projectile is in the coils, then the switching devices will have less current to make and break as the power is shifted along with the projectile.

To decrease further any possibility of undesirable current surges between coils and capacitors, the three-phase currents are generated in single-phase machines which are mechanically locked together so that the one hundred and twenty degree phase relation is maintained.

As explained under the subject “The Use of Electric Condensers or Capacitors,” the number of capacitors used depends only on the requirement that the electrostatic energy be kept equal to the electromagnetic energy. Hence, series resonance is as economical as parallel resonance.

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