Motion Picture News (Jul - Sep 1930)

36 Moliou Picture News Sept c in b er 27 , 1 9 3 (t THE Projectionists' Round Table By John F. Rider WE KNOW that the presence of a condenser in an A.C: circuit will manifest an influence which will control the value of the current through the circuit. We further know that this controlling action is a function of frequency. Namely that the reactance of the condenser, sometimes known as the permittance is a function of the frequency and of the capacity. \\ e noted that when a voltage is impressed across a resistance, the current in the circuit is limited by the resistance and that a certain amount of power is expended in the resistance. What are the power relations in an alternating circuit containing only a condenser with negligible resistance. As to the statement relative to the resistance, the condition of a 90° current lead is in itself an indication of a perfect capacity. Any deviation from this condition would produce a current lead of less than 90". As a matter of fact the absolute action in the ordinary condenser is such that the current lead is not 90°. Each and every condenser possesses a certain amount of resistance. However, this resistance is usually of such small value that it i classed a being negligible and the theoretical state of perfection is assumed. The power in a circuit is equal to the instantaneous value of e x i at that instant. 1 f we refer to figure J51C, we note that at four instants during a complete cycle the product of ei is O. These instants are at the 0° when the current is maximum and the voltage is zero; at the 90° point when the voltage is maximum and the current is zero; at the 189° when the voltage is zero and the current is maximum and at the 270° point when the current is zero and the voltage is maximum. Further, between the points 0° and 90°, the product of e x i is positive (above the zero line), and between the points 90° and 180°, it is negative because e is positive and i is negative. A similar condition exists between the 180° and 270° points and between the 270° and 360° points. If we multiply the instantaneous values of ei, we would secure a power curve such as that shown in figure 61 C. The heights of these curves represent the value of the power at each instant during the cycle. Energy is taken from the supply during the first quarter of the cycle, i.e. between the 0° and the (xi points and the average value of the power loop within this period is equal to the average power taken from the line, and the area of this loop represents the total amount of energy stored within the condenser during that period. Continuing with time, we note that during the next quarter cycle between the 90° and the 180° . points, the condenser is discharging, since the applied voltage is gradually decreasing, and the power loop is negative. Now, the average value of this loop, is the average power during this cycle and the area of tins loop is the total amounl of energy FED BACK into the supply by the condenser. We said that the theoretical condenser has no losses. If now. the total energy taken from the supply during one pari oi the cj cle is re turned to the supplj during the next quarter of a cycle, thi rom the sup ply during a completi cycli is ero. i ording to the power expended in the circuit is I' M OS 0 and since the phase difference P = FI , 90 = 0 Condenser ami Resistance hi Series. — Let us now assume a case where the capacity is not perfect. Let us say that an appreciable amount of resistance is present in the active surfaces of the capacity and between the connecting leads to the active plates. Such a condition is the equivalent of a perfect condenser with a series resistance. It is also possible to imagine a circuit containing a resistance in series with a capacity without any special reference to the coniditon of the condenser. The schematic of such an arrangement is as shown in figure 61D, where R is a resistance of 10 ohms and C is a large capacity of 1000 microfarads. The value of E is 110 volts. An examination of this circuit brings to light two significant facts. From what was said in connection with resistance and capacity, Rider Discusses Condensers Power in condenser circuits and the effect of a resistance in series with a condenser are the highlights of Lesson 18, in John Rider's "Sound Projection Course" which rippears weekly in MOTION PICTURE NEWS. Rider follows up with a discussion on the retarding offect of ;tn inductance in nn A.C. circuit, inductive reactance, impedance in A.C. circuits, concluding with in investigation on the power relation n ;.n A.C. circuit containing ',nly ..n .iductance. we note two controlling agents, namely the resistance and the capacity. Both of these will have some effect upon the magnitude of current which shall How in the circuit. Each one offers a certain amount of opposition and the two combined, offer a total amount of hindrance. The resistance R offers a certain amount of resistance, whereas the capacity C offers a i ertain amount of reactance. At first glance one would imagine that by adding the resistance and the reactance in ordinary algebraic fashion, that is 1\ in ohms + the reactance of C in ohms would afford the total hindrance. Such is not the case because of the phase relation existing between current and voltage with a resistance in the circuit and with a capacity in the circuit. The current and voltage are in phase across the resistance, but the current leads the voltage across the capacity. We must now determine a new value, one which would take into consideration the phase relation between the current and voltage with two such elements m series in the circuit, a value which would represent the total hindrance to current flow, by all the elements in the circuit. This value is known as the IMPEDANCE, and in this case has two components, the resistance of K .mil tin reactance of C. Let us continue and determine the relations present in this circuit. applied = 1 Id volts R = 10 ohms 1 = 1000 microfarads F = (ill cycles i Xc of the circuit is I ,IHII I. Xc = < 60 X 1000 = 2.65 ohms Because of the phase relation, the total opposition or hindrance introduced by the elements must be determined by adding the equivalent resistance value ( individual opposition effects) at right angles or vectorially, such as would be employed to determine the hypothenuse of a right triangle. Knowing the resistance of R and the reactance of C the total hindrance or IMPEDANCE of the circuit (designated by the capital letter Z) is Z = VR2 + Xc2 = VR)2 + 2.65 = 10.34 ohms A previous statement was made that when a capacity only is used in an A.C. circuit the current in that circuit is E Xc which is a form of Ohm's law. When the circuit contains more than one element and the total hindrance is the impedance Z of that circuit, the value of I is determined in a similar manner but R in" Ohm's law is now replaced by Z, viz : E 1 = and if we substitute the above values Z 110 10.34 = 10.638 amperes* (We shall call this value 10.64 amperes.) According to the definition of wrhat constitutes a series circuit, 10.64 amperes of current flows through R and C. We have two voltage drops in this circuit, that across R and that across C or Xc, hence IR and IXc. Now. as in the case of total hindrance, the sum of IR and IXc does not equal the E applied. While it is true that a voltmeter which will indicate A.C. voltages when connected across R and C will show that IR = 10.64 X 10 = 106.4 volts and IXc = 10.64 X 2.65 = 28.19 volts the arithmetic sum of these voltage is greater than the applied. But when added vectoriallv. E = VIR2 + IXc2 = V106.42 + 28. 192 = 110 volts Now. while the theoretical condition of a 90° current lead in the condenser holds true in the condenser, the phase difference between the current and voltage in the complete circuit is neither 90° as determined by the condenser or (I as determined by the resistance.. It is some value between 0° and 90° and current leading because of the predominating influence of the condenser. The power factor of the circuit is resistance R 10 cos G = — — ■ = = impedance 7. 10 34 = .967 and 6 = 14.75° *** ***(When cos 6 is known, reference to a table of natural sines and cosines will show the value of (») The power dissipated in the circuit is P = E I X cos G = 110 X 10.64 X .967 = 1132 watts The power dissipated may also be determined i n in This Is Lesson 18 in The Rider Series on Sound Projection