Motion Picture News (Jul - Sep 1930)

S e pte m her 27 , 19 3 0 Motion Picture News 3/ p = pr = 10.642 X 10 = 1132 watts. A.C. Circuit Containing Inductance Only. — We are somewhat familiar with the reaction present when a voltage is applied across an inductance. We know that the current does not instantaneously rise to its maximum value, that it lags behind the voltage. This property is utilized in many ways. Before showing the application of inductance, let us consider the action in an A.C. circuit which contains only inductance. Such a circuit is impossible in actual practice since every inductance consists of wire and wire has resistance. However, for the sake of clarity we can assume a perfect inductance without resistance. Suppose that such a coil were connected across a source of A.C. as in figure 62A. A current meter is connected to indicate the current in the circuit and we also have a voltmeter which indicates the voltage in the circuit. One such voltmeter is connected across the line and one meter across the inductance. We assume that the periodicity of the line supply voltage is sufficiently low to enable visual observation upon the meters of the variations in magnitude of the voltage and ccrrent. Let us further imagine that the line voltage is applied at the instant when it is zero in the curve. In other words E applied is zero. Now we know from the discussion of inductances in D.C. circuits that when current is caused to flow through an inductance, an emf of self induction is developed. W shall designate this voltage as Ex in the curve. Keeping in mind that the inductance is theoretically free from resistance, the first small increment of voltage applied causes the greatest flow of current through the circuit, since there is as yet no reaction in the system. Thus the applied . P<M£P* f 10 OHMS IO0OMFO. wltage E and the emf of self inductance El are both zero and the current II is maximum. \s the line voltage starts to increase in the negative direction, there occurs a change in current and this change of flux creates an emf of self induction across the inductance. This is El. This voltage is of such direction that it tends to stop the change of the current II and to send current in the opposite direction. There is therefore a gradual reduction in the magnitude of current flowing through the coil. As the applied voltage E increases still more, there continues to be a change of current and a change of flux, gradually increasing the emf of self-induction and gradually decreasing the current through the coil. When the applied voltage is maximum, the voltage El is also maximum and since these two voltages are of equal magnitude and opposite in effect, the current thr nigh the coil is zero. Now, as the voltage applied starts to decrease, there occurs a change in the voltage across the coil and current starts to flow. As the voltage E decreases still more, the emf of seli induction likewise decreases as the retarding effect upon the current flow also decreases. At the time when the applied voltage E is zero, the voltage El is also zero and the current II is maximum. At this instant, the current is stationary at its value and since there is no change of flux there can be no voltage developed across the co,il. Such is the start of the cycle as shown in figure 62B. Now, if we consider that the voltage applied and the voltage across the coil are maximum and the current is zero, we note that the voltage E passes t-IOON/ 60 CYCLES L FIG-6IP through its zero point 90° ahead of the current, or that the current lags the voltage by 90° in an inductive circuit, i.e. when the inductance has negligible resistance. Referring once more to figure 62B, the value of the current IL must be such that the reaction voltage, the emf of self induction will be equal to the applied voltage. Expressed in another manner, the emf of self-induction is the current limitation agent in the circuit. If we start with m applied E and MM EL at maximum values, the current changes from 0 to maximum in one quarter cycle arid during this period the emf of self-induction likewise changes from maximum to zero. Since the frequency is f cycles, the period during winch the aforementioned changes take place is Y^i second. Now, the emf of self induction depends upon two quantities. First, the turns in the coil, or the inductance of the coil, designated as L. Second, by the time rate of change of the current. This is shown in the curve. Since the current remains constant for an instant at its maximum value there is no change of flux and there is no voltage induced in the turns of the inductance, hence no El. Accordingly, the average voltage across the inductance during that quarter cycle is Eav. = L X (Im/l/4f) (60) = L X I m X 4f (a) Als Em = — X Eav (b) Therefore Em = — X L X Im X 4f (c) 2 which is = 2-n-f X L X Im (d) and Eeff. = 2wf X L X leff (e) and the current in the circuit is. in effective values, E I = (61) 2wF X L Suppose we imagine that L in figure <<2.\ is 10 henrvs and the frequency of E applied is 60 cycles. The maximum current in the circuit is 1 ampere. Substituting into equation 60, Eav. = 10 X_ (1/1/240) The value 1/240 is seccred as follows. If the line frequency is 60 cycles per second, the duration of a cycle is 1/60 second and one quarter of a cycle is 1/240 second. Now, the term 1/1/240 is the reciprocal of the reciprocal, which becomes the whole number since 1/240 is equal to .004166 and 1/. 004166 is equal to 240. Hence 4f is equal to 240, since f is 60, and equation 60 a becomes Eav. = 10 X 240 = 2440 volts The quantity ir/2 is equal to 3.1416/2 or 1.5707. Then equation 60b becomes Em = 2400 X 1.5707 = 3770 volts and equation 60b and c are the same. The quantity (^/2) X 4f is equal to the angular velocity 27rf, hence equation 60d becomes Em = 6.28 X 60 X 10 X 1 = 377 X 10 X 1 = 3770 volts and since Eeff = .707 X,Em and Ieff. = .707 X Im then equation 60e becomes Eeff. = 377 X 10 X .707 = 2665 volts and equation 61 becomes 2665 I = _3770 = .707 ampere effective. As is evident in equation 61, the term 2vrfl., is the equivalent of R in Ohm's Law for current. As was stated in connection with capacity reaction, this term is the inductance re action and is also stated as reactance and expressed in ohms. Just as capacity reactance is expressed by the capital letter X and the subscript C, inductive reactance is also designated by the capital letter X, but the subscript is L, thus Inductive Reactance = Xl = 27rf L (62) Now, if we examine this equation, we note two peculiarities. Both are opposite to that related to capacity reactance. Whereas capacity reactance decreases with frequency, inductive reactance is proportional to frequency. If the inductance is constant, and the frequency is doubled, the reactance will increase twofold. If the frequency is half constant and the inductance is doubled, the reactance will increase twofold. If both inductance and reactance are doubled, the reactance increases four-fold. On the other hand if the inductance is halved and the frequency is doubled, there will be no change in the reactance. The inductive reactance is independent of current just so long as the value of L is not altered by the presence of the current. Such is the case with all air core inductances. In some cases, iron core inductances which carry current are subject to changes of L with changes of the current values. As to the resistance of the coil (inductance), it has no effect upon the reactance. It controls other factors and aids in the limitation of the total current in the circuit but it has no bearing upon the reactance of the coil. Thus, if we have a coil rated at 100 henrvs and a resistance of 5000 ohms and that coil is to be used upon a frequency of 100 cvcles, the reactance Xl = 6.28 X 100 X 100 = 62800 ohms The resistance of 5000 ohms, represented the resistance of the wire used in the making of FIG. 62 C the coil is another quantity to be discussed shortly. Power in Circuit Employing an Inductance Only. — We determined that a condenser in an A.C. circuit consumes no power, that is a theoretically perfect condenser. Let us see what happens when the circuit contains inductance only, a theoretically perfect inductance. Referring to figure 62C, that the product of E I when. E is zero and I is maximum is 0. However, as E increases and I decreases, the instantaneous values of e x i represent power. But at the 90° point, the power is again zero and this is repeated at the 180° point, the 270° point and the 360° point. Between these specified points we have power in the circuit. Now, we stated that the inductance was free from resistance, hence, there is no power lost as heat developed in the resistance. Since the increase of current through the inductance represents power taken from the circuit and stored in the magnetic field, and the decrease of current through the inductance represents the collapse of the magnetic field and restoration of the power to the supply circuit, the power loops shown in figure 62C, indicate that the amount taken from the circuit is again restored to the circuit and there is no power loss in the inductance. The phase angle 9 between the voltage E and the current T is 90° and since the power P = E X I X cos O and cos 90° = 0 therefore P = E X I X cos e = 0 power in watts and the power factor = 0