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though the source of magnetic flux remains fixed in one place.
The electromagnetic induction of electric current is the underlying principle of generators and transformers: the former utilizing mechanically-rotated magnets of constant strength, and the latter fixed magnets of fluctuating strength. It is obvious that the net result is the same in both cases: currents are induced by magnetic fields cutting through conductors.
Because the magnetic fields produced by a steady d-c are non-varying in intensity, no electromagnetic induction occurs in a d-c circuit unless means are provided for rapidly varying the strength of the current. When a-c is considered, however, we encounter pronounced self-induction, or inductance, effects.
Effects of Inductance
Assume that a choke is connected to a suitable source of d-c. (A choke is a coil of wire wound around a core of soft iron.) The coil impedes the flow of d-c by virtue of its resistance — the resistance of the wire. The value of the resistance is easily calculated by Ohm's law when we know the voltage-drop and the current passed:
R
and the power formula gives the number of watts dissipated in the resistance as heat:
P = EI When the same choke is connected to a source of a-c neither the Ohm's law formula nor the power formula hold good. The mathematical product of voltmeter and ammeter readings will not be the true power consumed by the choke.
Indeed, the true watts (measured by a wattmeter) will be vastly less than the apparent watts obtained by multiplying volts by amperes.
This strange state of affairs is due to the induction of an opposing e.m.f. in the choke. Why opposing? An important principle known as Lenz's law tells us that an induced current always flows in such a direction that it opposes (counteracts) the magnetic field of the original current. The net result of the two currents (the applied and the induced) flowing in the same circuit is a time-displacement between volts and amperes.
In other words, the volt-peaks and the ampere-peaks no longer coincide. All inductive devices (chokes, electromagnets, transformers, motors, etc.) cause the current changes to lag behind the voltage changes. Curve B in Fig. 2 shows a 90-degree current lag.
An inductance shifts the phase in this manner because the induction of current is greatest when the applied current is changing most rapidly, that is, when it passes through the zero point. We thus find that the induced voltage flows in a direction opposite to the supplied current during the intervals of falling current: hence the current changes are said to lag behind the voltage changes by 90 degrees in a purely inductive circuit.
Since in practice there is always some resistance in a circuit, the current lag due to inductance may approach, but never reach, a full 90 degrees.
Wattless Current
Current having an "angle of phase difference" approaching 90 degrees (current lagging or leading by nearly 90 degrees) is called "wattless" current. Such a current is obtained when we feed a-c
CINEMA NORMANDIE, PARIS
One of the best European installations, this room is 30 by 15 feet and utilizes a 140-foot throw.
Equipment includes a Western Electric M-2 sound system (3 machines); Simplex projectors, Peerless
lamps, Hertner Transverter, and a Brenkert effect projector. Installation by Westrex.
(A)
(B)
,*Volts
Amperes
180°
>-Volts Amperes ^270°
180°
Volts
O" 90
-I Amperes-*
360°
FIG. 2. Alternating current curves: (A) e.m.f. and current in phase; (6) current lagging by 90 degrees; (C) current leading by 90 degrees.
to the primary of a transformer whose secondary circuit is open.
Voltmeter and ammeter readings taken on the "live" primary circuit will indicate a heavy consumption of electric power, but the watts found by multiplying volts by amperes are largely apparent watts. (The word apparent as applied to watts means "seeming.") The out-of-phase components of the wattless current merely surge in and out of the transformer without the expenditure of power.
It is for this reason that the primary of a doorbell transformer may be permanently connected to the 110-voIt a-c line. Except when the volt and ampere components are brought into phase by taking power from the secondary, as by ringing a doorbell, the power consumption of the transformer is negligible. Because inductance does not figure in a d-c circuit, the transformer would quickly burn up if connected to a source of 110 volts of d-c!
Power Factor
In order to calculate the power dissipated in an a-c circuit (true watts), we must multiply the product of volts times amperes by a factor called the power factor of the circuit. The power factor is the cosine of the angle of phase difference between current and e.m.f., which angle is represented by the Greek letter phi, </>.
Vtrue = EI cos d>
The cosine of 90° of current lag or lead is 0, hence in wattless current the value of the true watts is obviously 0. When current and e.m.f. are in phase (that is, when volt and ampere-peaks coincide), the phase angle is 0°; and since cos 0° is 1, the value of the true watts is the full product of volts multiplied by amperes, just as with d-c.
The quotient obtained by dividing true watts (determined with a wattmeter) by the product of volts times amperes (sep(Continued on page 29)
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INTERNATIONAL PROJECTIONIST • January 1949