Fig. 433.—A circuit containing a choke coil.
Let Fig. 433 represent a choke coil. Since alternating current is used, the magnetic field is continually changing. Each turn of wire has its own magnetic field. The lines of force of turn number 1 expand and contract and as they do so they move across turns 2, 3 and so on. In like manner the lines of force from each turn of wire move across the other turns. In other words the coil is cutting its own lines of force. Now whenever an electric conductor cuts magnetic lines of force an electromotive force is induced in the conductor. There is then an e.m.f. induced in the coil by its own magnetic field. This induced e.m.f. on the whole opposes the applied e.m.f.; in the primary of our bell ringing transformer the induced e.m.f. opposes the e.m.f. of the line to such an extent as to reduce the current almost to zero. Inductance is the action of an alternating current in inducing an opposing e.m.f. in the coil in which the current is flowing. Since this opposing e.m.f. is induced in the coil by its own magnetic field this action is also called self-induction. In a transformer the action of the field of the primary upon the secondary is mutual induction; while the action of the field of the primary in choking the current in the primary itself is self-induction or inductance. A coil having a single winding and used to introduce inductance in a circuit is called a choke coil. A choke coil inserted in a lamp circuit in series with the lamps dims the lamps because it reduces the intensity of the current.
Fig. 434.—Diagram showing graphically an alternating current with a "lag" of 30° behind its electromotive force.
Self-induction causes the current to lag, that is, the current does not quite reach its maximum at the instant the voltage reaches its maximum. Fig. 434 shows graphically an e.m.f. and a lagging current. In this figure the maximum current is shown following the maximum voltage at an interval of 30 degrees. In other words the armature in a two-pole field must turn 30 degrees from the position of maximum voltage before the current in the coil, where the self-induction occurs, reaches its maximum.
434. Reactance and Impedance.—A choke coil has resistance as well as inductance. Its resistance can be found by the voltmeter-ammeter method, using a direct current. (See Art. 278.) Let us take for example the primary winding of a bell ringing transformer. Using a direct current and testing the coil with a voltmeter and ammeter we find its resistance to be, let us say, one ohm. If we connect the same coil across a 110 volt a.-c. line we find the current to be very small, say 0.05 ampere. The coil now has resistance and reactance. Reactance is the effect of self-induction in hindering the flow of current. It is measured in ohms. The combined effect of resistance and reactance is called impedance. In the example above, the coil has 110 (volts)/0.05 (ampere) = 2200 ohms of impedance. In applying Ohm's law to an alternating current circuit, impedance must be substituted for resistance. Ohm's law as applied to an a-c. circuit should be stated: "Current intensity equals e.m.f. divided by impedance", or I = E/Z. (Z = impedance.)
Fig. 435.—The relation between resistance, reactance and impedance.
Impedance, however, does not equal the sum of resistance and reactance. The relation between these three quantities is similar to that between the three sides of a right triangle, in which the impedance represents the hypotenuse, and the resistance and reactance the other two sides. See Fig. 435 which indicates that Resistance2 + Reactance2 = Impedance2, or (R2 + X2 = Z2). (X = reactance.) To illustrate this relation; suppose the primary of a transformer has 10 ohms impedance and 8 ohms resistance, then the reactance equals 102 - 82 = 62, or the reactance is 6 ohms.