Volume I Part 4 (2/2)

The unit of electrostatic capacity is the _farad_. As this unit is inconveniently large, for practical applications the unit _microfarad_--millionth of a farad--is employed. If quant.i.ties are known in microfarads and are to be used in calculations in which the values of the capacity require to be farads, care should be taken to introduce the proper corrective factor.

The electrostatic capacity between the conductors of a telephone line depends upon their surface area, their length, their position, and the nature of the materials separating them from each other and from other things. For instance, in an open wire line of two wires, the electrostatic capacity depends upon the diameter of the wires, upon the length of the line, upon their distance apart, upon their distance above the earth, and upon the specific inductive capacity of the air.

Air being so common an insulating medium, it is taken as a convenient material whose specific inductive capacity may be used as a basis of reference. Therefore, the specific inductive capacity of air is taken as unity. All solid matter has higher specific inductive capacity than air.

The electrostatic capacity of two open wires .165 inch diameter, 1 ft. apart, and 30 ft. above the earth, is of the order of .009 microfarads per mile. This quant.i.ty would be higher if the wires were closer together; or nearer the earth; or if they were surrounded by a gas other than the air or hydrogen; or if the wires were insulated not by a gas but by any solid covering. As another example, a line composed of two wires of a diameter of .036 inch, if wrapped with paper and twisted into a pair as a part of a telephone-cable, has a mutual electrostatic capacity of approximately .08 microfarads per mile, this quant.i.ty being greater if the cable be more tightly compressed.

The use of paper as an insulator for wires in telephone cables is due to its low specific inductive capacity. This is because the insulation of the wires is so largely dry air. Rubber and similar insulating materials give capacities as great as twice that of dry paper.

The condenser or other capacity acts as an effective barrier to the steady flow of direct currents. Applying a fixed potential causes a mere rush of current to charge its surface to a definite degree, dependent upon the particular conditions. The condenser does not act as such a barrier to alternating currents, for it is possible to talk through a condenser by means of the alternating voice currents of telephony, or to pa.s.s through it alternating currents of much lower frequency. A condenser is used in series with a polarized ringer for the purpose of letting through alternating current for ringing the bell, and of preventing the flow of direct current.

The degree to which the condenser allows alternating currents to pa.s.s while stopping direct currents, depends on the capacity of the condenser and on the frequencies of alternating current. The larger the condenser capacity or the higher the frequency of the alternations, the greater will be the current pa.s.sing through the circuit. The degree to which the current is opposed by the capacity is the reactance of that capacity for that frequency. The formula is

Capacity reactance = 1 /_C_[omega]

wherein _C_ is the capacity in farads and [omega] is 2[pi]_n_, or twice 3.1416 times the frequency.

All the foregoing leads to the generalization that the higher the frequency, the less the opposition of a capacity to an alternating current. If the frequency be zero, the reactance is infinite, _i.e._, the circuit is open to direct current. If the frequency be infinite, the reactance is zero, _i.e._, the circuit is as if the condenser were replaced by a solid conductor of no resistance. Compare this statement with the correlative generalization which follows the next thought upon inductance.

Inductance of the Circuit. Inductance is the property of a circuit by which change of current in it tends to produce in itself and other conductors an electromotive force other than that which causes the current. Its unit is the _henry_. The inductance of a circuit is one henry when a change of one ampere per second produces an electromotive force of one volt. Induction _between_ circuits occurs because the circuits possess inductance; it is called _mutual induction_.

Induction _within_ a circuit occurs because the circuit possesses inductance; it is called _self-induction_. Lenz' law says: _In all cases of electromagnetic induction, the induced currents have such a direction that their reaction tends to stop the motion which produced them_.

[Ill.u.s.tration: Fig. 32. Spiral of Wire]

[Ill.u.s.tration: Fig. 33. Spiral of Wire Around Iron Core]

All conductors possess inductance, but straight wires used in lines have negligible inductance in most actual cases. All wires which are wound into coils, such as electromagnets, possess inductance in a greatly increased degree. A wire wound into a spiral, as indicated in Fig. 32, possesses much greater inductance than when drawn out straight. If iron be inserted into the spiral, as shown in Fig. 33, the inductance is still further increased. It is for the purpose of eliminating inductance that resistance coils are wound with double wires, so that current pa.s.sing through such coils turns in one direction half the way and in the other direction the other half.

A simple test will enable the results of a series inductance in a line to be appreciated. Conceive a very short line of two wires to connect two local battery telephones. Such a line possesses negligible resistance, inductance, and shunt capacity. Its insulation is practically infinite. Let inductive coils such as electromagnets be inserted serially in the wires of the line one by one, while conversation goes on. The listening observer will notice that the sounds reaching his ear steadily grow faint as the inductance in the line increases and the speaking observer will notice the same thing through the receiver in series with the line.

Both observations in this test show that the amount of current entering and emerging from the line decreased as the inductance increased. Compare this with the test with bridged capacity and the loading of lines described later herein, observing the curious beneficial result when both hurtful properties are present in a line.

The test is ill.u.s.trated in Fig. 34.

The degree in which any current is opposed by inductance is termed the reactance of that inductance. Its formula is

Inductive reactance = _L_[omega]

wherein _L_ is the inductance in henrys and [omega] is _2_[pi]_n_, or twice 3.1416 times the frequency. To distinguish the two kinds of reactance, that due to the capacity is called _capacity reactance_ and that due to inductance is called _inductive reactance_.

All the foregoing leads to the generalization that the higher the frequency, the greater the opposition of an inductance to an alternating current. If the frequency be zero, the reactance is zero, _i.e._, the circuit conducts direct current as mere resistance. If the frequency be infinite, the reactance is infinite, _i.e._, the circuit is ”open” to the alternating current and that current cannot pa.s.s through it. Compare this with the correlative generalization following the preceding thought upon capacity.

[Ill.u.s.tration: Fig. 34. Test of Line with Varying Serial Inductance]

Capacity and inductance depend only on states of matter. Their reactances depend on states of matter and actions of energy.

In circuits having both resistance and capacity or resistance and inductance, both properties affect the pa.s.sage of current. The joint reaction is expressed in ohms and is called _impedance_. Its value is the square root of the sum of the squares of the resistance and reactance, or, Z being impedance,

------------------------- / 1 Z = / R^{2} + ---------------- / C^{2}[omega]^{2}

<script>