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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 22 CHAPTER Inductive Circuits
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Topics Covered in Chapter 22 Sine-Wave i L Lags v L by 90° X L and R in Series Impedance (Z) X L and R in Parallel
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Topics Covered in Chapter 22 (continued) Q of a Coil AF and RF Chokes The General Case of Inductive Voltage
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RL Voltage and Current Series Circuit The sine-wave voltage drop across an inductor leads the inductor’s current by 90°. The sine-wave ac voltage across a resistor is always in phase with its current. The total sine-wave ac voltage for a series RL circuit always leads the total current by an angle between 0° and 90°.
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VRVR I Waveforms and Phasors for a Series RL Circuit I I VLVL Note: since current is constant in a series circuit, the current waveforms and current phasors are shown in the reference positions.
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Source Voltage and Current Phasors Note: the source voltage leads the current by an amount proportional to the ratio of inductive reactance to resistance. I VSVS X L < R I VSVS X L = R I VSVS X L > R I VSVS
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Phasors for Series RL Circuits VRVR VLVL VTVT Voltage Phasors R XLXL ZTZT Impedance Phasor
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I = 2 A The Impedance of a Series RL Circuit V S = 100 R = 30 X L = 40 504030 22 2 2 L XRZ R XLXL The impedance is the total opposition to current flow. It’s the phasor sum of resistance and reactance in a series circuit A Z V I S 2 50 100 Z
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The Tangent Function opposite adjacent Negative angle opposite adjacent Positive angle
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I = 2 A The Phase Angle of a Series RL Circuit V S = 100 R = 30 30 40 50 53 30 40 11 Tan R X L V S leads I by 53° X L = 40 I VLVL VSVS 53°
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KVL in a Series RL Circuit 60 V 80 V 100 V V R = IR = 2 x 30 = 60 V V L = IX L = 2 x 40 = 80 V VVV ST 1008060 22 I = 2 A V S = 100 R = 30 X L = 40
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RL Voltage and Current Parallel Circuit The sine-wave ac current for an inductor lags the inductor’s voltage drop by 90°. The sine-wave ac voltage across a resistor is always in phase with its current. The total sine-wave ac current for a parallel RL circuit always lags the applied voltage by an angle between 0° and 90°.
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Current Phasors for Parallel RL Circuits IRIR ILIL ITIT
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Currents in a Parallel RL Circuit V S = 120 R = 30 X L = 40 IRIR ILIL I T = 5 A ITIT A R V I S R 4 30 120 A X V I L S L 3 40 120 AIII LRT 534 22 22
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Phase Angle in a Parallel RL Circuit 4 A 3 A5 A 37 4 3 11 Tan I I R L The total current lags the source voltage by 37°. I T = 5 A V S = 120 R = 30 X L = 40
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Impedance in a Parallel RL Circuit 24 5 120 T S EQ I V Z 4 A 3 A5 A I T = 5 A V S = 120 R = 30 X L = 40
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Summary of R, X L, and Z Resistance (R) in Ohms, Voltage in phase with current. Inductive Reactance (X L ) in Ohms, Voltage leads current by 90°.
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Summary of R, X L, and Z (continued) Series Circuit Impedance (Z T ) in Ohms, Voltage leads current. Becomes more inductive with increasing f. Becomes more resistive with decreasing f. Parallel circuit impedance (Z EQ ) in Ohms, Voltage leads current. Becomes more resistive with increasing f. Becomes more inductive with decreasing f.
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Summary of Formulas for R, X L, and Z Series RLParallel RL fLX L 2 22 LRT VVV 2 2 LT XRZ R X Tan L fLX L 2 22 LRT III T S EQ I V Z R L I I Tan
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The Q of a Coil XLXL riri e L i L R X r X Q At higher frequencies, skin effect increases the conductor resistance. Eddy current loss and hysteresis loss in iron-core coils increase as f goes up. R e increases with frequency because of skin effect, eddy current loss, and hysteresis loss. Coils achieve their maximum Q at some frequency and then it drops at higher frequencies.
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