1. Basic Electronics Ninth Edition Grob Schultz
©2002 The McGraw-Hill Companies

2. Basic Electronics Inductive Reactance 21 Ninth Edition CHAPTER
©2003 The McGraw-Hill Companies

3. Topics Covered in Chapter 21
How XL Reduces the Amount of I
XL = 2pfL
Series and Parallel Inductive Reactances
Ohm's Law and XL
Applications of XL for Different Frequencies
Waveshape of vL Induced by Sine-Wave Current

4. Definitions
Inductive reactance is the opposition an inductor offers to the flow of sinusoidal current.
Symbol: XL
Units: Ohms
Formula: X fL L = 2 p

5. Factors Affecting XL
The value of XL is proportional to the value of inductance:
Increasing L increases XL
Decreasing L decreases XL
The value of XL is proportional to the frequency:
Increasing f increases XL
Decreasing f decreases XL

6. Factors affecting alternating current flow
XL = 2fL
XL = 2fL
Less reactance means more current flow.

7. Summary of XL Formulas fL X p 2 = When f and L are known:
When XL and f are known: L X f p 2 =
When XL and L are known:

8. Inductive Reactances in Series
Total reactance is the sum of the individual reactances.
XLT = XL1 + XL2 + XL etc.
All reactances have the same current.
The voltage across each reactance equals current times reactance.
VXL1 = I ´ XL1

9. Inductive Reactances in Series
5 mH L1
1 kHz
2 mH L2
LT = 17 mH
10 mH L3
XL1 = 2fL1 = 6.28 x 1x103 x 5x10-3 = 31.4 W
XL2 = 2fL2 = 6.28 x 1x103 x 2x10-3 = 12.6 W
XL3 = 2fL3 = 6.28 x 1x103 x 10x10-3 = 62.8 W
XLT = 2fLT = 6.28 x 1x103 x 17x10-3 = 107 W
XLT = = 107 W

10. Ohm’s Law KVL check: 31.4 + 12.6 + 62.8 = 107 V 5 mH L1 1 kHz 107 V
LT = 17 mH
10 mH L3
I = V/XLT = 107/107 = 1 A
VL1 = IXL1 = 1 x 31.4 = 31.4 V
VL2 = IXL2 = 1 x 12.6 = 12.6 V
VL3 = IXL3 = 1 x 62.8 = 62.8 V
KVL check: = 107 V

11. Inductive Reactances in Parallel
Total reactance is found by the reciprocal formula: 1 2 3 X
etc LT L = + K .
All reactances have the same voltage.
The current through each reactance equals voltage divided by reactance:
IL = VL / XL

12. Inductive Reactances in Parallel
1 kHz
107 V
5 mH
2 mH
10 mH
LEQ = 1.25 mH
IL1 = 107/XL1 = 107/31.4 = 3.4 A
IL2 = 107/XL2 = 107/12.6 = 8.5 A
IL3 = 107/XL3 = 107/62.8 = 1.7 A
IT = 107/XLEQ = 107/7.85 = 13.6 A
KCL check: = 13.6 A

13. Inductance vs. Inductive Reactance
Symbol is L
Unit is H
Value depends on construction
L = vL / (di/dt)
Inductive Reactance
Symbol is XL
Unit is W
Value depends on L and f
XL = vL / iL or 2pfL

14. di/dt for Sinusoidal Current is a Cosine Wave
Iinst. = Imax x cos  dt di L v =
Current 
Sinusoidal Current

15. Inductive Reactance vs. Resistance
Symbol is XL
Unit is W
Value increases for higher f
Current lags voltage by 90°, q = 90°
Resistance
Symbol is R
Unit is W
Value does not change with f
Current and voltage are in phase, q = 0°

16. Inductor Voltage and Current
Amplitude
Time V I
q = -90 V I

17. Resistor Voltage and Current
Amplitude
Time I V
q = 0 V I

18. Capacitor Voltage and Current
q = 90 V
Amplitude
Time V I