Transcript Chapter20

Chapter
20
Inductive Reactance
Topics Covered in Chapter 20
20-1: How XL Reduces the Amount of I
20-2: XL = 2πfL
20-3: Series or Parallel Inductive Reactances
20-4: Ohm's Law Applied to XL
20-5: Applications of XL for Different Frequencies
20-6: Waveshape of vL Induced by Sine-Wave Current
© 2007 The McGraw-Hill Companies, Inc. All rights reserved.
20-1: How XL Reduces
the Amount of I
 An inductance can have appreciable XL in ac circuits
to reduce the amount of current.
 The higher the frequency of ac, and the greater the L,
the higher the XL.
 There is no XL for steady direct current. In this case,
the coil is a resistance equal to the resistance of the
wire.
McGraw-Hill
© 2007 The McGraw-Hill Companies, Inc. All rights reserved.
20-1: How XL Reduces
the Amount of I
 In Fig. 20-1 (a), there is no inductance,
and the ac voltage source causes the bulb
to light with full brilliance.
 In Fig. 20-1 (b), a coil is connected in
series with the bulb.
 The coil has a negligible dc resistance of
1 Ω, but a reactance of 1000 Ω.
 Now, I is 120 V / 1000 Ω, approximately
0.12 A. This is not enough to light the bulb.
 In Fig. 20-1 (c), the coil is also in series
with the bulb, but the battery voltage
produces a steady dc.
 Without any current variations, there is no
XLand the bulb lights with full brilliance.
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Fig. 20-1:
20-2: XL = 2πfL
 The formula XL = 2πfL includes the effects of





frequency and inductance for calculating the inductive
reactance.
The frequency is in hertz, and L is in henrys for an XL
in ohms.
The constant factor 2π is always 2 x 3.14 = 6.28.
The frequency f is a time element.
The inductance L indicates the physical factors of the
coil.
Inductive reactance XL is in ohms, corresponding to a
VL/IL ratio for sine-wave ac circuits.
20-3: Series or Parallel
Inductive Reactances
 Since reactance is an opposition in ohms, the values XL in series or in
parallel are combined the same way as ohms of resistance.
 With series reactances, the total is the sum of the individual values as
shown in Fig. 20-5 (a).
 The combined reactance of parallel reactances is calculated by the
reciprocal formula.
Fig. 20-5
20-4: Ohm's Law Applied to XL
The amount of current in an ac circuit with only inductive reactance is equal
to the applied voltage divided by XL.
I = V/XL = 1 A
I = V/XLT = 0.5 A
Fig. 20-6:
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I1 = V/XL1 = 1 A
I2 = V/XL2 = 1 A
IT = I1 + I2 = 2 A
20-5: Applications of XL
for Different Frequencies
 The general use of inductance is to provide minimum
reactance for relatively low frequencies but more for
higher frequencies.
 If 1000 Ω is taken as a suitable value of XL for many
applications, typical inductances can be calculated for
different frequencies. Some are as follows:
 2.65 H
 160 mH
 16 mH
 1.6 μH
60 Hz
10,000 Hz
10,000 Hz
100 MHz
Power-line frequency
Medium audio frequency
High audio frequency
In FM broadcast band
20-6: Waveshape of vL
Induced by Sine-Wave Current
 Induced voltage depends on rate of change of current
rather than on the absolute value if i.
 A vL curve that is 90° out of phase is a cosine wave of
voltage for the sine wave of current iL.
 The frequency of VL is 1/T.
 The ratio of vL/iL specifies the inductive reactance in
ohms.
20-6: Waveshape of vL
Induced by Sine-Wave Current
di/dt for Sinusoidal Current is a Cosine Wave
di/dt
Current
vL = L
di
dt

0
Sinusoidal Current
Iinst. = Imax × cos 
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20-6: Waveshape of vL
Induced by Sine-Wave Current
Amplitude
Inductor Voltage and Current
0
Time
Θ = -90
I
V
I
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V
20-6: Waveshape of vL
Induced by Sine-Wave Current
Application of the 90° phase angle in a circuit
 The phase angle of 90° between VL and I will always
apply for any L with sine wave current.
 The specific comparison is only between the induced
voltage across any one coil and the current flowing in
its turns.
20-6: Waveshape of vL
Induced by Sine-Wave Current
 Current I1 lags VL1 by 90°.
 Current I2 lags VL2 by 90°.
 Current I3 lags VL3 by 90°.
NOTE: I3 is also IT for the seriesparallel circuit.
Fig. 20-8