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

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Presentation on theme: "Basic Electronics Ninth Edition Basic Electronics Ninth Edition ©2002 The McGraw-Hill Companies Grob Schultz."— Presentation transcript:

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

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

3 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

4 Definitions Inductive reactance is the opposition an inductor offers to the flow of sinusoidal current. Symbol: X L Units: Ohms Formula: XfL L  2 

5 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

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

7 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:

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

9 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 = = 107  Inductive Reactances in Series X L T = 2  fL T = 6.28 x 1x10 3 x 17x10 -3 = 107 

10 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: = 107 V 2 mH 5 mH 10 mH L T = 17 mH L1L1 L3L3 L2L2 1 kHz 107 V

11 Inductive Reactances in Parallel Total reactance is found by the reciprocal formula: 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

12 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: = 13.6 A

13 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

14 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 

15 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°

16 Inductor Voltage and Current Amplitude 0  I V I V Time

17 Resistor Voltage and Current Amplitude 0  I V V Time I

18 Capacitor Voltage and Current Amplitude 0  I V I V Time


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