Fig. 4 



9)f 



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 



T 



145 



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 



