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chapter 11 Inductors Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 11 1 The Basic Inductor When a length of wire is formed into a coil., it becomes a basic inductor. When there is current in the inductor, a three-dimensional magnetic field is created. A change in current causes the magnetic S N field to change. This in turn induces a voltage across the inductor that opposes the original change in current. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 11 1 The Basic Inductor One henry is the inductance of a coil when a current, changing at a rate of one ampere per second, induces one volt across the coil. Most coils are much smaller than 1 H. The effect of inductance is greatly magnified by adding turns and winding them on a magnetic material. Large inductors and transformers are wound on a core to increase the inductance. Magnetic core Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 11 1 Faraday’s law Faraday’s law was introduced in Chapter 7 and repeated here because of its importance to inductors. The amount of voltage induced in a coil is directly proportional to the rate of change of the magnetic field with respect to the coil. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 11 1 Lenz’s law Lenz’s law was also introduced in Chapter 7 and is an extension of Faraday’s law, defining the direction of the induced voltage: When the current through a coil changes and an induced voltage is created as a result of the changing magnetic field, the direction of the induced voltage is such that it always opposes the change in the current. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 11 1 Lenz’s law A basic circuit to demonstrate Lenz’s law is shown. Initially, the SW is open and there is a small current in the circuit through L and R1. L VS SW + R1 R2 Electronics Fundamentals 8th edition Floyd/Buchla + © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 11 1 Lenz’s law SW closes and immediately a voltage appears across L that tends to oppose any change in current. L + VS + SW R1 R2 Electronics Fundamentals 8th edition Floyd/Buchla + Initially, the meter reads same current as before the switch was closed. © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 11 1 Lenz’s law After a time, the current stabilizes at a higher level (due to I2) as the voltage decays across the coil. L VS SW + R1 R2 + Later, the meter reads a higher current because of the load change. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 11 1 Types of inductors There are a variety of inductors, depending on the amount of inductance required and the application. Some, with fine wires, are encapsulated and may appear like a resistor. Common symbols for inductors (coils) are Air core Electronics Fundamentals 8th edition Floyd/Buchla Iron core Ferrite core Variable © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 11 1 Factors affecting inductance Four factors affect the amount of inductance for a coil. The equation for the inductance of a coil is N 2 A L l where L = inductance in henries N = number of turns of wire = permeability in H/m (same as Wb/At-m) l = coil length on meters Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 11 1 What is the inductance of a 2 cm long, 150 turn coil wrapped on an low carbon steel core that is 0.5 cm diameter? The permeability of low carbon steel is 2.5 x104 H/m (Wb/At-m). A πr 2 π 0.0025 m 7.85 105 m2 2 N 2 A L l 2 150 t 2.5 104 Wb/At-m 7.85 105 m2 0.02 m 22 mH Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 11 1 Series inductors When inductors are connected in series, the total inductance is the sum of the individual inductors. The general equation for inductors in series is LT L1 L2 L3 ...Ln If a 1.5 mH inductor is connected in series with an 680 H inductor, the total inductance is 2.18 mH Electronics Fundamentals 8th edition Floyd/Buchla L 1 L 2 1 . 5 m H 6 8 0 H © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 11 1 Parallel inductors When inductors are connected in parallel, the total inductance is smaller than the smallest one. The general equation for inductors in parallel is LT 1 1 1 1 1 ... L1 L2 L3 LT The total inductance of two inductors is LT 1 1 1 L1 L2 …or you can use the product-over-sum rule. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 11 1 Parallel inductors If a 1.5 mH inductor is connected in parallel with an 680 H inductor, the total inductance is 468 H L1 1.5m H Electronics Fundamentals 8th edition Floyd/Buchla L2 680 H © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 11 1 Inductors in dc circuits When an inductor is connected in series with a resistor and dc source, the current change is exponential. Vinitial t 0 Inductor voltage after switch closure Ifinal R L 0 Current after switch closure Electronics Fundamentals 8th edition Floyd/Buchla t © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 11 1 Universal exponential curves L τ R 100% 95% 99% Rising exponential 63% 60% 40% 37% Falling exponential 20% 14% 5% 0 0 Electronics Fundamentals 8th edition Floyd/Buchla 98% 86% 80% Percent of final value Specific values for current and voltage can be read from a universal curve. For an RL circuit, the time constant is 1t 2% 2t 3t 4t Number of time constants 1% 5t © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 11 1 Inductive reactance Inductive reactance is the opposition to ac by an inductor. The equation for inductive reactance is X L 2πfL The reactance of a 33 H inductor when a frequency of 550 kHz is applied is 114 W Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 11 1 Inductive reactance When inductors are in series, the total reactance is the sum of the individual reactances. That is, X L(tot ) X L1 X L2 X L3 X Ln Assume three 220 H inductors are in series with a 455 kHz ac source. What is the total reactance? The reactance of each inductor is X L 2 fL 2 455 kHz 220 μH 629 W X L(tot ) X L1 X L2 X L3 629 W 629 W 629 W 1.89 kW Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 11 1 Inductive reactance When inductors are in parallel, the total reactance is the reciprocal of the sum of the reciprocals of the individual reactances. That is, X L(tot ) 1 1 1 1 1 X L1 X L2 X L3 X Ln If the three 220 H inductors from the last example are placed in parallel with the 455 kHz ac source, what is the total reactance? The reactance of each inductor is 629 W X L(tot ) Electronics Fundamentals 8th edition Floyd/Buchla 1 1 210 W 1 1 1 1 1 1 + + X L1 X L2 X L3 629 W 629 W 629 W © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 11 1 Inductive phase shift When a sine wave is applied to an inductor, there is a phase shift between voltage and current such that voltage always leads the current by 90o. Electronics Fundamentals 8th edition Floyd/Buchla VL 0 90 I 0 © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 11 1 Power in an inductor True Power: Ideally, inductors do not dissipate power. However, a small amount of power is dissipated in winding resistance given by the equation: Ptrue = (Irms)2RW Reactive Power: Reactive power is a measure of the rate at which the inductor stores and returns energy. One form of the reactive power equation is: Pr=VrmsIrms The unit for reactive power is the VAR. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 11 1 Q of a coil The quality factor (Q) of a coil is given by the ratio of reactive power to true power. I2XL Q 2 I RW For a series circuit, I cancels, leaving XL Q RW Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 11 1 Quiz 1. Assuming all other factors are the same, the inductance of an inductor will be larger if a. more turns are added b. the area is made larger c. the length is shorter d. all of the above Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 11 1 Quiz 2. The henry is defined as the inductance of a coil when a. a constant current of one amp develops one volt. b. one volt is induced due to a change in current of one amp per second. c. one amp is induced due to a change in voltage of one volt. d. the opposition to current is one ohm. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 11 1 Quiz 3. The symbol for a ferrite core inductor is a. b. c. d. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 11 1 Quiz 4. The symbol for a variable inductor is a. b. c. d. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 11 1 Quiz 5. The total inductance of a 270 H inductor connected in series with a 1.2 mH inductor is a. 220 H b. 271 H c. 599 H d. 1.47 mH Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 11 1 Quiz 6. The total inductance of a 270 H inductor connected in parallel with a 1.2 mH inductor is a. 220 H b. 271 H c. 599 H d. 1.47 mH Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 11 1 Quiz 8. For circuit shown, the time constant is L a. 270 ns 2 7 0 H b. 270 s c. 270 ms V S 1 0V R 1 .0k W d. 3.70 s Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 11 1 Quiz 10. If a sine wave from a function generator is applied to an inductor, the current will a. lag voltage by 90o b. lag voltage by 45o c. be in phase with the voltage d. none of the above Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 11 1 Quiz Answers: Electronics Fundamentals 8th edition Floyd/Buchla 1. d 6. a 2. b 7. b 3. d 8. a 4. c 9. c 5. d 10. a © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved.