Fig. 4
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��Popular Science Monthly
ohmsj into the alternator electromotive force in volts. This is true for any fre- quency, except for comparatively small changes in the resistance.
If instead of the resistance there is connected a coil having inductance, L in Fig. 3, a very different condition holds. This circuit possesses inductive react- ance of an amount in ohms equal to 6.28 times the frequency of the current times the inductance of the coil m henry s. If the alternator frequency is 100,000 per second and the coil has 5 millihenrys (or 5/1000 of a henry) inductance, the inductive reactance is 6.28 times 100,000 times 5/1000, or 3140 ohms. Assuming the resistance to be zero, if the alter- nator produces 100 volts, only 100/3140 or 0.0318 of an ampere will flow. Thus for this frequency the sim- ple coil of wire presents more effective resistance than would a straight car- bon rod of 3,000 ohms. It should be noted that the higher the frequency goes the greater becomes the re- actance, and therefore the impedance, of a coil. At pig. 5
zero frequency, which is I direct current, the react- ance vanishes and the im- pedance of the coil is merely its resistance. 1 ^j
Still another condition ' ^JUUUUlf
holds if a condenser is con- Fig. 6
nected in the circuit, as in Fig. 4. The circuit now has what is called capacity reactance, and this, in ohms, amounts to the reciprocal of 6.28 times the frequency times the capacity in farads. ' If the frequency is 100,000 per second and the capacity is 0.0005 microfarad (or 5/10,000,000,000 farad), the capacity reactance figures out 6.28 times 100,000 times 5/10,000,000,000 di- vided into I, or 0.000314 divided into i, or 3.180 ohms. This would permit about one-thirtieth of an ampere to flow if 100 volts at 100,000 cycles were applied. The most important thing to note as to capac- ity reactance is that it decreases as the size of the condenser increases, and as the applied frequency increases. It is
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in efrect an exact opposite of inductive reactance, and each may be used to neu- tralise the current limiting characteristic of the other.
This opposition of capacity and induct- ance reactances is one of the most im- portant phenomena made use of in radio telegraphy, and is the basis of resonance. The action may be illustrated by study- ing Figure 5, where a condenser and an inductance are connected in series with the alternator and ammeter. Assuming resistance still to be zero and remember- ing that the eft'ective reactance in ohms is equal to the inductive reactance minus the capacity reactance, or vice versa, the remainder taking the name, of the larger component. This is found to be 3180 minus 3140 ohms, or only 40 ohms ca- pacity reactance. In the circuit of Fig. 5, therefore, a voltage of 100 at 100,000 cycles would cause 2.5 am- peres to flow through the condenser and inductance in series. This is over 750 times as much current as would flow through either the condenser or the coil alone, and is made possible by the neutralizing effect above stated. If the con- denser were of slightly more than 0.0005 micro- farad capacity, so as to make its capacity reactance exactly equal numerically to the inductive reactance, these two ele- ments would neutralize completely, for the total reactance would be zero. If the resistance were also zero there would be no limit to the current in the circuit ; in practice there is always some resist- ance in circuit, and this determines the number of amperes which will flow through the circuit for a given voltage, if the resonant condition exists.
Fig. 6 shows the practical closed cir- cuit of capacity, inductance and resist- ance. The current in amperes equals the e. m. f. in volts divided by the im- pedance in ohms. The impedance equals the square root of the sum of the square of the resistance and the square of the
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