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

Basic Electronics Ninth Edition Basic Electronics Ninth Edition ©2003 The McGraw-Hill Companies 22 CHAPTER Inductive Circuits

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

Topics Covered in Chapter 22 (continued)  Q of a Coil  AF and RF Chokes  The General Case of Inductive Voltage

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°.

 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.

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

Phasors for Series RL Circuits VRVR VLVL VTVT Voltage Phasors  R XLXL ZTZT Impedance Phasor 

I = 2 A The Impedance of a Series RL Circuit V S = 100 R = 30  X L = 40   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  Z

The Tangent Function  opposite adjacent Negative angle  opposite adjacent Positive angle

I = 2 A The Phase Angle of a Series RL Circuit V S = 100 R = 30  30  40  50     Tan R X L  V S leads I by 53° X L = 40  I VLVL VSVS 53°

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  I = 2 A V S = 100 R = 30  X L = 40 

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°.

Current Phasors for Parallel RL Circuits IRIR ILIL ITIT 

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  A X V I L S L  AIII LRT 

Phase Angle in a Parallel RL Circuit 4 A 3 A5 A    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 

Impedance in a Parallel RL Circuit   T S EQ I V Z 4 A 3 A5 A I T = 5 A V S = 120 R = 30  X L = 40 

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°.

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.

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 

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.