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 illustrated 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 pass through it.  Compare this with the correlative generalization following the preceding thought upon capacity.

[Illustration:  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 passage 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}

and

--------------------------
Z =  /  R^{2} + L^{2}[omega]^{2}
\/

the symbols meaning as before.

In words, these formulas mean that, knowing the frequency of the current and the capacity of a condenser, or the frequency of the current and the inductance of a circuit (a line or piece of apparatus), and in either case the resistance of the circuit, one may learn the impedance by calculation.