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**Basic Electronics Ninth Edition Grob Schultz**

©2002 The McGraw-Hill Companies

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**Basic Electronics Inductive Reactance 21 Ninth Edition CHAPTER**

©2003 The McGraw-Hill Companies

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**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

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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

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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

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**Factors affecting alternating current flow**

XL = 2fL XL = 2fL Less reactance means more current flow.

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**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:

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**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

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**Inductive Reactances in Series**

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

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**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

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**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

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**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

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**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

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**di/dt for Sinusoidal Current is a Cosine Wave**

Iinst. = Imax x cos dt di L v = Current Sinusoidal Current

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**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°

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**Inductor Voltage and Current**

Amplitude Time V I q = -90 V I

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**Resistor Voltage and Current**

Amplitude Time I V q = 0 V I

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**Capacitor Voltage and Current**

q = 90 V Amplitude Time V I

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