Motion Picture News (Oct-Dec 1930)

October 4, 1 930 !THE' *1/ olio ii P i c I ii r e N i w s 101 Projectionists' Round Table By John F. Rider JF the theoretically perfect inductance consemes no power, yet limits the flow of current through the circuit, what is the effect of a practical form of inductance consisting of inductance and resistance. A. C. Circuit Containing Inductance and Resistance.— We know from past work that the presence of a resistance in any circuit displays a controlling effect upon the current in that circuit. We have found that the reaction due to the presence of an inductance in an A. C. circuit will also display a controlling effect upon the current in that circuit. Suppose that we consider these two forces in one circuit and note the effect. Since both resistance and reactance are oppositions to the flow of current, the combined effect is going to be the total hindrance or IMPEDANCE of the circuit. Suppose that we have the units shown in figure 62D, arranged as shown. The resistance R of 10 ohms is in series with an inductance L of 10 henrys. The combination is connected across a 60-cycle circuit with an alternating voltage E of 100 volts. According to the law for series circuits, there is only one path for the current in this circuit and whatever the value of this current, it flows through the resistance and the inductance. According to equation 62 Xl = 6.28 c 60x10 = 3770 ohms and R = ohms To determine the current in the circuit we cannot add Xl and R because of the phase relation between the current and voltage through the resistance and the inductance. They must be added vectorially to determine the total hindrance or impedance. Therefore Z = VR2 + Xl2 = V102 + 37702 = 3770 + ohms *** *** When the reactance is equal to many times the resistance, so that the ratio between the resistance and the reactance is very small, or when the ratio between the reactance and the resistance is very great, as in this case, 377: 1 it is customary to employ the reactance value as the impedance value, where Xl = Z. Thus in the above example, the total impedance inclusive of the resistance is between 3770 and 3770.5 ohms, making the value of R negligible with respect to its current limiting action. and IR = .0265 x 10 = .265 volts ioohms 10 HENevs L 60CYCUES FIG. 63 A If we say that Z = 3770 ohms 100 then I = = .0265 ampere 3770 This value of current flows through the resistance R and the reactance Xl. There are then two drops in the circuit, the IR drop and the IXl drop. IXl=. 0265x3770 = 99.9 volts These values of voltage would be indicated upon A.C. voltmeter connected across the resistance R and the inductance L, respectively. However the sum of these two voltages is not equal to the impressed voltage. The voltage applied is the vector sum of the voltages across Theatres and Electrics The effect of a resistance in series with an inductance and impedance of A.C. circuit with restistance and inductance, highlight John Rider's current lesson in the theatre sound projection course, which appears every week in MOTION PICTURE NEWS, exclusively. Further discussions in this article involve A.C. circuit containing resistance, capacity and inductance in series, and the relation between frequency, capacity, inductance and reactance. A thorough investigation of the topics concerning series resonance, voltage step-up in series resonant circuit and application of series resonant circuits conclude this installment. R and L, thus Eapp. = V(IR)2+ (IXl)2 The power factor of the circuit is R R cos 0 = = Z \/R2 + Xl* 3770 = .00265 and 0 = 89° 5' = 89.85° lag on the part of the current *** The difference of .15° representing about 9' is due to the presence of the resistance R. If we consider that the resistance of the inductance L is 10 ohms and it has no other resistance, then the unit may be classed as being practically perfect. The power in the circuit is P = EI x cos 6 = 100 x .0265 x .00265 = .007 watt It might be well at this time to consider another case of an inductance in series with a resistance, wherein the effect of the resistance is more pronounced. The circuit remains as in 62D, except that the value of the resistance is 1000 ohms and the value of the inductance is 1 henry. Then R= 1000 ohms and Xl = 377 ohms and Z = V10002 + 3772 = 1069 ohms*** *** The effect of the reactance is less than that of the resistance, with respect to the total impedance. 100 I = = .0935 ampere 1069 then IR = 93.5 volts and IXl = 35.25 volts The power factor of the circuit is R 1000 cos O = = = .935 Z 1069 and 6 = 20.7° current lag The power in the circuit is P = E x I x cos 0 = 100 x .0935 x .935 = 8.74 watts also P = I2R = 09352 x 1000 = 8.74 watts. A.C. Circuit Containing Capacity, Inductance and Resistance in Series — We have noted certain significant facts about resistance, capacity and inductance employed in A.C. circuits and have combined resistance and capacity and resistance and inductance. Let us now combine resistance, capacity and inductance into one circuit as in figure 64. When three such elements are in one circuit, we encounter three states of phase difference, across the resistance, across the capacity and across the inductance. Across the resistance the current and voltage are in phase. Across the capacity the current leads the voltage by 90° and across the inductance the current lags the voltage by 90J. Since the phase difference across the condenser and the inductance are directly reversed, there must be some reaction due to this difference when these two elements are combined in one circuit. If we recall a definite state in connection with current and voltage reactions in capacitative and inductive circuits, we can appreciate the relation between the voltage across the capacity and the voltage across the inductance. Suppose that we take as the basis the state of maximum current in the circuit. At that instant the voltage across the resistance will be maximum since E and I are in phase. However, the currents leads the voltage across the capacity by 90 degrees and when the current is maximum the voltage across the condenser will be zero. Then again, the current lags the voltage across an inductance by 90° and when the current is maximum and voltage across the inductance is zero. Continuing, when ifV J r> -^'"' • ' \ FIG. 636 the current is zero through the capacity of the inductance, the voltage across the capacity is maximum and the voltage across the inductance is maximum. However, because of the respective phase relations, these voltages are acting in opposite directions and can be shown as in figure 63B. IXl is the voltage across the inductance L. The curve IXc shows the voltage across the condenser C and the (Continued on next page) This Is Lesson 19 in The Rider Series on Sound Projection