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Z1 Z2 Zn
PF = R/z Questions
1. Explain what inductance is.
2. Explain what inductive reactance is.
3. Give the formula for inductive reactance.
4. Explain the effect of induced emf.
5. Explain fully what impedance is.
6. In a circuit with inductive reactance, does the current lead or lag?
7. IX Z = ?
8. I X R = ?
9. I X XL =?
10. Give the formula for Z.
234 Chapter 20
11. Wattmeters read power. (True or false?)
12. The voltmeter reading times the ammeter reading gives power. (True or false?)
13. Real Power/Apparent Power = ?
14. Explain power factor fully.
15. Does inductive reactance cause a leading or lagging power factor?
16. Three impedances, A, B, C, are connected in parallel in a 60-Hz circuit. Impedance A has 200 ohms’ resistance. Impedance B has 60 ohms’ resistance and an inductance of 0.5 henry.
(a) What is the combined impedance? (b) What is the power factor? (c) What is the current in each branch at 120 volts? (d) What is the combined current in all three branches at 120 volts?
17. A coil possessing 10 ohms’ resistance and 8 ohms’ inductive reactance is connected in series with a coil of 25 ohms’ resistance and 12 ohms’ inductive reactance. What voltage will be required to force 5 amperes through this circuit?
Capacitance in AC Circuits
Capacitors and capacitance were thoroughly covered in theory in an earlier chapter. These both play a very important part in AC circuits and calculations.
Analogy of Capacitor Action
Figure 21-1 is an analogy of how AC apparently flows through a capacitor. In reality it doesn’t flow through the capacitor, but the results are very similar to its flowing through the capacitor. A rubber diaphragm (D) forms a tight seal and may be compared to the dielectric of a capacitor. The upper and lower halves of the enclosure (C) may be compared to the two plates of a capacitor. Regions X and Y may be compared to conductors connected to the two plates of the capacitor, and plunger P may be compared to an AC source.
Figure 21-1 Analogy illustrating how AC can apparently flow through a capacitor.
When plunger P goes down, fluid moves in Y toward diaphragm D and the diaphragm is forced into position A. This may be compared to a current charge in a capacitor. Plunger P then moves up and the fluid in X flows toward diaphragm D from the underside of D back through Y to the plunger, and diaphragm D goes to position B.
A capacitor reverses plate charges every alternation in an AC circuit.
236 Chapter 21
Beginning with a simple circuit, as in Figure 21-2, will aid in a better understanding of cause and effect. Here there is an ammeter, A, two capacitor plates, C and D, dielectric K, battery B, and switch S.
Switch S is open, plates C and D possess no electrical charge, and ammeter A reads zero. At the moment switch S is closed there is an inrush of current from battery B into plate D, charging it negative. Electrons from plate C go back through ammeter A to battery
B. The maximum current results at the instant the switch S is closed and tapers off to zero as the plates become charged. The major point here is that there is maximum current when there is no charge in the capacitor.
The capacitance of a capacitor is fixed by its construction and is proportional to three things:
1. Size and shape of the plates
2. Thickness of the dielectric
3. Material of the dielectric
It will be recalled that a capacitor has a capacitance of 1 farad, when 1 ampere flowing for 1 second raises its potential 1 volt.
Figure 21-2 Current surge into a capacitor.
Q = charge in one plate in coulombs E = voltage applied across capacitor in volts C = capacitance in farads
Capacitance in AC Circuits 237
Current and Voltage Relations
In Figure 21-3, the relationship of current and applied voltage, as they appear in a capacitor, will be shown. You will recall that when the voltage was first applied to a capacitor, the current was its greatest. This was illustrated in Figure 21-2. Now, referring to Figure 21-3, the applied voltage starts at zero and moves in time from 0 to B, and in voltage from 0 to C. The voltage rises rapidly and it is found that the current during this interval, DE, is near maximum rate. At point F the voltage is at maximum, so at this point (F) there is no voltage change and no current (G), but the quantity of charge in the capacitor is maximum. Here, since the capacitor is fully charged, there is no current. Also, we see that the voltage of the capacitor is maximum at M and in opposite polarity to the applied voltage. (The voltage across the capacitor acts so as to buck the applied voltage.) When the applied voltage, F to T, falls off, the voltage across the capacitor will cause a reversal of current from G to N.
Figure 21-3 Relationship of line current, applied voltage, and counter emf in a circuit with capacitive reactance.