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

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

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Topics Covered in Chapter 21 How X L Reduces the Amount of I X L = 2 fL Series and Parallel Inductive Reactances Ohm's Law and X L Applications of X L for Different Frequencies Waveshape of v L 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: X L Units: Ohms Formula: XfL L 2

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

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Factors affecting alternating current flow Less reactance means more current flow. X L = 2 fL

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Summary of X L Formulas When f and L are known: f X L L 2 L X f L 2 fLX L 2 When X L and f are known: When X L and L are known:

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Inductive Reactances in Series Total reactance is the sum of the individual reactances. X LT = X L1 + X L2 + X L3 +... + etc. All reactances have the same current. The voltage across each reactance equals current times reactance. V XL1 = I X L1

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2 mH 5 mH 10 mH L T = 17 mH L1L1 L3L3 L2L2 1 kHz X L 1 = 2 fL 1 = 6.28 x 1x10 3 x 5x10 -3 = 31.4 X L 2 = 2 fL 2 = 6.28 x 1x10 3 x 2x10 -3 = 12.6 X L 3 = 2 fL 3 = 6.28 x 1x10 3 x 10x10 -3 = 62.8 X L T = 31.4 + 12.6 + 62.8 = 107 Inductive Reactances in Series X L T = 2 fL T = 6.28 x 1x10 3 x 17x10 -3 = 107

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V L 1 = IX L 1 = 1 x 31.4 = 31.4 V Ohm’s Law I = V/X L T = 107/107 = 1 A V L 2 = IX L 2 = 1 x 12.6 = 12.6 V V L 3 = IX L 3 = 1 x 62.8 = 62.8 V KVL check: 31.4 + 12.6 + 62.8 = 107 V 2 mH 5 mH 10 mH L T = 17 mH L1L1 L3L3 L2L2 1 kHz 107 V

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Inductive Reactances in Parallel Total reactance is found by the reciprocal formula: 1111 123 XXXX etc LTLLL . All reactances have the same voltage. The current through each reactance equals voltage divided by reactance: I L = V L / X L

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Inductive Reactances in Parallel 10 mH2 mH 5 mH L EQ = 1.25 mH 1 kHz 107 V L1L1 L3L3 L2L2 I L 1 = 107/X L 1 = 107/31.4 = 3.4 A I L 2 = 107/X L 2 = 107/12.6 = 8.5 A I L 3 = 107/X L 3 = 107/62.8 = 1.7 A I T = 107/X L EQ = 107/7.85 = 13.6 A KCL check: 3.4 + 8.5 + 1.7 = 13.6 A

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Inductance vs. Inductive Reactance Inductance Symbol is L Unit is H Value depends on construction L = v L / (di/dt) Inductive Reactance Symbol is X L Unit is Value depends on L and f X L = v L / i L or 2 fL

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di/dt for Sinusoidal Current is a Cosine Wave Current 0 di/dt I inst. = I max x cos Sinusoidal Current dt di Lv L

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

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Inductor Voltage and Current Amplitude 0 I V I V Time

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Resistor Voltage and Current Amplitude 0 I V V Time I

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Capacitor Voltage and Current Amplitude 0 I V I V Time

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