Motion Picture News (Oct-Dec 1930)

50 Motion Picture N ew s O ctober 11 , 1930 amplification is secured within the coupling unit of which C and L are a part. Power m a Series Circuit at Resonance. — It has been shown that IXl = IXc at resonance and since they are opposite in effect, the total voltage across both elements is zero. Consequently, the voltage impressed is used to overcome the reaction of the resistance R in the circuit. The voltage and current are in phase and the energy dissipated in the circuit, or as is usually expressed, the power expended in the circuit is that developed in the form of heat across the resistance. There is no power loss in the capacity or the inductance. This condition was illustrated in the curves published in the preceding installment and erroneously labeled Figure 64. Parallel Circuit Consisting of Inductance, Capacity and Resistance. — Since capacity, inducandtance and resistance are individual elements, they may be combined in parallel as easily as in series. Such a parallel combination is shown in Figure 66A. R is the resistance, C is the capacity and L is the inductance. All are connected between the same two points in the circuit, consequently these elements are in parallel. Since they are in parallel, the same volt x. fig. 65 B age is impressed across each element and it is possible to determine the current through each branch by considering each element as a separate entity. Thus, if we assign the following numerical values; R is 6 ohms, C is 50 mfds., L is .15 henry, E is 100 volts and F is 100 cycles, we can determine the current through each branch. Thus : 100 Ir = = 10 amperes 10 100 II = = 1.06 ampere 94 100 Ic = = 3.14 ampere 31.8 If the above combination consisted of three resistances and the applied voltage were of D.C. character, resolution of the total current would be simple arithmetic, the sum of the individual branch currents. However, we are concerned with A.C. and varied phase relations. We know from past discussion that the current and voltage are in phase across the resistance R. On the other hand, the current leads the voltage across the capacity and lags the voltage across the inductance. Such a condition was observed in the simple series circuit. From past discussion we further know that the reactions due to the presence of the inductance and that, due to the presence of the capacity, are in the opposite direction. Because of the opposite effects of the current flow through an inductance and through a capacity, that is, when both are shown related to the same impressed voltage, the resultant current must be the difference between these two currents. At this time we are neglecting the current through the resistance. Previous mention to the current in the inductive branch and the current in the capacitative branch can be clarified by attempting to visualize the conditions in the circuit. We h 7. 3 d D 0 LOWER HIGHER. RESONANCE FKEQUEHCY FIG.660 naturally have a total current which divides between the branches in a certain manner. If we neglect the current through the resistance branch and appreciate that the instantaneous effects of the inductive and the capacitative branches are opposite, it is possible to have current in the main circuit and no current through the combination of the capacity and the inductance in parallel. There naturally will be current in each branch, but since they tend to neutralize each other, the combined current will be less than the current in either branch. If it so happens that the currents are equal in these two branches, the resultant current is zero. If, on the other hand, the value of current in one branch is greater than the current in the other branch, the difference between these two will SOURCE 1 L ABSORBER OF p OF POWER. t Power. represent the resultant current in the branches. The total current in the circuit shown in Figure 66A i sthe vector sum of the individual branch currents or I« = VlR::+ (Ic — Il)s If we substitute the numerical values of current previously determined, It = Vl0"-| (3.14 — 1.06)a = 10.2 amperes The total impedance of the circuit is E I Now, this value of 10.2 amperes is less than the arithmetical sum of the individual branch currents and if by chance, the frequency of the line supply is changed to say 5S.1 cycles, at which time the reactance of L would be 54.7 ohms and that of C would likewise be 54.7 ohms, the current in the inductive branch would FIG. 65C be equal to the current in the capacitative branch and, since their directions are opposite and they are equal, they neutralize and the current in the main circuit would be that due to the resistance R, namely 10 amperes and once agains, Ohm's law would be applicable or E " R Referring once more to the original solution of the currents, the current through the capacity is greater than that through the inductance. A certain amount of the capacity reaction overcomes the inductive reaction, and there remains an amount of capacity reaction. The resultant current represents the condition as if the combination of the inductance and capacity were a capacity only, of such value as to cause the flow of the resultant current. This will become clearer as we consider the effect of frequency. At this time, we can say that if, for example, the resultant current of the combination of L and C at 100 cycles and with the voltage applied is such that Ic — II is equal to 2.08 amperes, the combination of L and C can be replaced by a capacity which when used at 100 cycles would have a value of reactance L PIG 65 E which would cause the flow of 2.08 amperes when the impressed voltage is 100 volts. More about this later. If we assume for the moment that R is absent and that Xl = Xc and further that the inductance L is free of resistance, the current in the inductive branch would equal the current in the capacitative branch. If they are opposite in action and neutralize each other, there would he no current in the main circuit. Such a condition of resonance produces an effect exactly opposite to that experienced with the series resonant circuit. In the parallel combination the impedance is theoretically infinite at resonance and decreases off resonance. If we show this relation in the form of curves, it would resemble the curve shown in Figure 66B and the current through the circuit would be as shown in Figure 66C. The reduction in impedance each side of the resonant frequency* is due to the fact that off resonance the currents in the two reactive branches are unequal. Below resonance, when the frequency is lowered, the capacity reactance increases and the inductive reactance decreases and the circuit as like an inductance. Above the resonant frequency, when the frequency is increased, the capacity reactance decreases and the inductive reactance increases. Therefore, more current flows through the capacity and the complete circuit acts like a capacity. When working with parallel circuits it is customary to quote the admittance of the circuit rather than the impedance. The term admittance represents the reciprocal of the impedance or I Y = Z When working with a parallel resonant circuit and in view of the fact that infinite impedance is impossible, it is customary to classify the FIG.66A FIG. 65" F