wave output is the result of one side of the generator loop cutting
lines of force. In the first half turn of rotation this produces a positive
current and in the second half of rotation produces a negative current.
This completes one cycle of AC generati
Reactive Components LIST OF FIGURES Figure 1 Current, Self-Induced
EMF, and Applied Voltage in Inductive
Circuit . 2 Figure 2 Coil Circuit and Phasor
Diagram . 3 Figure 3 Voltage, Charge, and Current
in a Capacitor . 5 Figure 4 Circuit and Phasor
Diagram
begins to charge in the opposite direction, and the voltage and
current are again in the same direction. Rev. 0 Page 5 ES-08
CAPACITANCE Basic AC Reactive Components At point d, the capacitor
is fully charged, and the current flow is again zero. From poin
impedance (Z) for that circuit. 1.12 Given a simple R-C-L series AC
circuit and the values for resistance (R), inductive reactance (XL), and
capacitive reactance (XC), CALCULATE the impedance (Z) for that
circuit. Rev. 0 Page v ES-08 OBJECTIVES Basic AC R
or by using a power triangle. 1.2 DEFINE power factor as it relates to
true power and apparent power. 1.3 Given the necessary values for
voltage (E), resistance (R), reactance (X), impedance (Z), and/or
current (I), CALCULATE the following power component
relationship between the two waves. Effective Values The output
voltage of an AC generator can be expressed in two ways. One is
graphically by use of a sine wave (Figure 3). The second way is
algebraically by the equation e=Emax sin t, which will be cover
maximum voltage, and the angular velocity, and is equal to the
output of an AC Generator. e E (7-11) max sin(t) ES-07 Page 8 Rev. 0
Basic AC Theory AC GENERATION ANALYSIS where e = induced EMF
(volts) Emax = maximum induced EMF (volts) = angular velocity
270 (point d), the flux change is also the greatest at those times.
Consequently, the self-induced EMF in the coil is at its maximum (or
minimum) value at these points, as shown in Figure 1. Because the
current is not changing at the point when it is goin
induced EMF in a circuit depends on how fast the flux that links the
circuit is changing. In the case of self-induced EMF (such as in a coil), a
counter EMF is induced in the coil due to a change in current and flux
in the coil. This CEMF opposes any chan
(point a to point c), the induced EMF is of opposite polarity to the
applied voltage and opposes the rise in current. Notice that as the
current passes through its zero value (point b) the induced voltage
reaches its maximum negative value. With the curre
effective current (A) E = effective voltage across the capacitive
reactance (V) XC = capacitive reactance () Example: A 10F capacitor
is connected to a 120V, 60Hz power source (see Figure 4). Find the
capacitive reactance and the current flowing in the ci
IMPEDANCE Basic AC Reactive Components where Z = impedance ()
R = resistance () X = net reactance () The relationship between
resistance, reactance, and impedance is shown in Figure 5. Figure 5
Relationship Between Resistance, Reactance, and Impedance The
0.707 (7-2) Peak value = average value x 1.57 (7-3) Effective value
(RMS) = average value x 1.11 (7-4) Peak value = effective value (RMS)
x 1.414 (7-5) Average value = effective (RMS) x 0.9 (7-6) The values of
current (I) and voltage (E) that are normally
OF TABLES LIST OF TABLES NONE Rev. 0 Page iii ES-08 REFERENCES
Basic AC Reactive Components REFERENCES Gussow, Milton, Schaums
Outline Series, Basic Electricity, McGraw-Hill. Academic Program for
Nuclear Power Plant Personnel, Volume IV, Columbia, MD: Gen
in time. At 120, e1 passes through the zero value, which is 60 ahead
of e2 (e2 equals zero at 180). The voltage e1 is said to lead e2 by 60
electrical degrees, or it can be said that e2 lags e1 by 60 electrical
degrees. Figure 5 Phase Relationship Rev. 0
Circuits and Machines, 5th Edition, McGraw-Hill. Croft, Carr, Watt, and
Summers, American Electricians Handbook, 10th Edition, McGraw-Hill.
Mason, C. Russel, The Art and Science of Protective Relaying, John
Wiley and Sons. Mileaf, Harry, Electricity One -
coil. The units of angular velocity are radians per second, and 2
radians is a full revolution. A radian is an angle that subtends an arc
equal to the radius of a circle. One radian equals 57.3 degrees. One
cycle of the sine wave is generated when the coi
leads applied voltage by 90o in a purely capacitive circuit. The phasor
diagram shows the applied voltage (E) vector leading (below) the
current (I) vector by the amount of the phase angle differential due to
the relationship between voltage and current i
perpendicular to the field and is cutting the greatest number of
magnetic lines of force. As the coil continues to turn, the voltage and
current induced decrease until they reach zero, where the coil is again
in the vertical position (Figure 2, 180o ). In
of these values, and then taking the square root. The effective value,
being the root of the mean (average) square of the currents, is known
as the root-mean-square, or RMS value. In order to understand the
meaning of effective current applied to a sine w
simple circuit. 1.3 DESCRIBE the effect of the phase relationship
between current and voltage in an inductive circuit. 1.4 DRAW a
simple phasor diagram representing AC current (I) and voltage (E) in
an inductive circuit. 1.5 DEFINE capacitive reactance (X
circuit. Capacitors The variation of an alternating voltage applied to
Figure 3 Voltage, Charge, and Current in a Capacitor a capacitor, the
charge on the capacitor, and the current flowing through the
capacitor are represented by Figure 3. The current fl
Rev. 0 Basic AC Theory AC GENERATION ANALYSIS Example 2: The peak
current in an AC circuit is 10 amps. What is the average value of
current in the circuit? Iav = 0.637 Imax Iav = 0.637 (10 amps) Iav = 6.37
amps Phase Angle Phase angle is the fraction of a
or radians) Example 1: What is the induced EMF in a coil producing a
maximum EMF of 120 V when the angle from reference is 45?
e=Emax sin e = 120 V (sin 45) e = 84.84 V The maximum induced
voltage can also be called peak voltage Ep. If (t) is the time in
period, and the number of cycles per second is called the frequency
(measured in hertz). One way to refer to AC voltage or current is by
peak voltage (Ep) or peak current (Ip). This is the maximum voltage or
current for an AC sine wave. Another value, the
of a given circuit is increased, the current flow will increase. It can also
be said that if the frequency or capacitance is increased, the
opposition to current flow decreases; therefore, capacitive reactance,
which is the opposition to current flow, is
seen to lag the current by 90. The value of the self-induced EMF
varies as a sine wave and lags the current by 90, as shown in Figure
1. The applied voltage must be equal and opposite to the self-induced
EMF at all times; therefore, the current lags the a
Calculate the impedance. ES-08 Page 12 Rev. 0 Basic AC Reactive
Components IMPEDANCE Figure 7 Simple R-C Circuit Solution: Z R 2 X
2 C 602 502 3600 2500 6100 Z 78.1 Impedance in R-C-L Circuits
Impedance in an R-C-L series circuit is equal to the phasor su