Chapt ha e pt r e r 11 Inductors

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1 Chapter 11 Inductors

2 The Basic Inductor When a length of wire is formed onto a coil, it becomes a basic inductor Magnetic lines of force around each loop in the winding of the coil effectively add to the lines of force around the adjoining loops, forming a strong electromagnetic field within and around the coil The unit of inductance is the henry (H), defined as the inductance when one ampere per second through the coil, induces one volt across the coil

3 Factors that determine the inductance of a coil Thomas L. Floyd Electronics Fundamentals, 6e Electric Circuit Fundamentals, 6e Copyright 2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

4 Inductors in DC Circuits When there is constant (DC) current in an inductor, there is no induced voltage There is a slight voltage drop in the circuit due to the winding resistance of the coil The coil basically appears as a short to DC

5 FIGURE 11-2 Symbol for the inductor. Basic Symbol for a Coil Thomas L. Floyd Electronics Fundamentals, 6e Electric Circuit Fundamentals, 6e Copyright 2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

6 FIGURE 11-9 Symbols for fixed and variable inductors. Thomas L. Floyd Electronics Fundamentals, 6e Electric Circuit Fundamentals, 6e Copyright 2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

8 Typical Inductors

9 Winding resistance of a coil The small inherent wire resistance is called the dc resistance or the winding resistance (RW) It is usually ignored Thomas L. Floyd Electronics Fundamentals, 6e Electric Circuit Fundamentals, 6e Copyright 2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

10 Winding capacitance of a coil When many turns of wire are placed close together in a coil, there is a winding capacitance (CW) CW may become significant at high frequencies Thomas L. Floyd Electronics Fundamentals, 6e Electric Circuit Fundamentals, 6e Copyright 2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

11 Self-Inductance Inductance is a measure of a coil s ability to establish an induced voltage as a result of a change in its current The induced voltage opposes the change in current (v ind )

12 Faraday s and Lenz s Laws Recall Faraday s law: 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 Recall Lenz s law: When the current through a coil changes: An induced voltage is created as a result of the changing electromagnetic field The direction/polarity of the induced voltage is such that it always opposes the change in current

13 Induced Voltage in the Series RL Circuit At the instant of switch closure, the inductor effectively acts as an open with all the source voltage across it During the first 5 time constants, the current is building up exponentially, and the induced coil voltage is decreasing The resistor voltage increases with current After 5 time constants, all of the source voltage is dropped across the resistor and none across the coil

14 Resistor and Coil Voltages in an Energizing Circuit Coil appears as an open Coil appears as a short Thomas L. Floyd Electronics Fundamentals, 6e Electric Circuit Fundamentals, 6e Copyright 2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

15 Resistor and Coil Voltages in a De-Energizing Circuit 10V instantaneously induced in the coil trying to keep current flowing in same direction After V ind decays, there is no current Thomas L. Floyd Electronics Fundamentals, 6e Electric Circuit Fundamentals, 6e Copyright 2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

16 RL Time Constant Because the inductor s basic action opposes a change in its current, it follows that current cannot change instantaneously in an inductor τ = L/R where: τ is in seconds (s) L is in henries (H) R is in ohms (Ω)

17 Exponential Formulas RL Time Constant = L/R The special formula for determining instantaneous current values for an RL circuit from zero is: i =I F (1 - e -Rt/L ) => I F (1 - ) The special formula for determining instantaneous current values an RL circuit to zero is: i =I i e -Rt/L => I i

18 Energizing Current in an Inductor In a series RL circuit, the current will increase to approximately 63% of its full value in one timeconstant (τ) interval after the switch is closed The current reaches its final value in approximately 5τ

19 Circuit Current in a an Energizing Circuit Thomas L. Floyd Electronics Fundamentals, 6e Electric Circuit Fundamentals, 6e Copyright 2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

20 Energizing current in an inductor Thomas L. Floyd Electronics Fundamentals, 6e Electric Circuit Fundamentals, 6e Copyright 2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

21 De-energizing Current in an Inductor In a series RL circuit, the current will decrease to approximately 37% of its fully charged value one time-constant (τ) interval after the switch is closed The current reaches 1% of its initial value in approximately 5τ; considered to be equal to 0

22 Circuit Current in a De-Energizing Circuit At t = 0, instantaneous current remains the same Thomas L. Floyd Electronics Fundamentals, 6e Electric Circuit Fundamentals, 6e Copyright 2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

23 De-energizing current in an inductor Thomas L. Floyd Electronics Fundamentals, 6e Electric Circuit Fundamentals, 6e Copyright 2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

24 Series Inductors When inductors are connected in series, the total inductance increases L T = L 1 + L 2 + L L n

25 Parallel Inductors When inductors are connected in parallel, the total inductance is less than the smallest inductance 1/L T = 1/L 1 + 1/L 2 + 1/L /L n

26 Inductors in AC Circuits An increase in frequency induces more voltage across the inductor in a direction to oppose the current and causes it to decrease in amplitude The polarity of induced voltage is such that the resulting induced current is in a direction that opposes the change in the magnetic field that produced it

27 Inductive Reactance Inductive reactance is the opposition to sinusoidal current, expressed in ohms The inductor offers opposition to current, and that opposition varies directly with frequency The formula for inductive reactance, X L, is: X L = 2πf L

28 The current in an inductive circuit varies inversely with the frequency of the source voltage Higher Frequency = Higher X L Thomas L. Floyd Electronics Fundamentals, 6e Electric Circuit Fundamentals, 6e Copyright 2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

29 For a fixed voltage and fixed frequency, the current varies inversely with the inductance value More Inductance = Higher X L Thomas L. Floyd Electronics Fundamentals, 6e Electric Circuit Fundamentals, 6e Copyright 2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

30 Phase Relationship of Current and Voltage in an Inductor The voltage leads inductor current by 90 (ELI) The current lags inductor voltage by 90 The curves below are for a purely inductive circuit

31 Current is always lagging the inductor voltage by 90º Current Lags the Voltage by 90 Deg V Or: Voltage Leads the Current by 90 Deg (ELI) I Thomas L. Floyd Electronics Fundamentals, 6e Electric Circuit Fundamentals, 6e Copyright 2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

32 Power in an Inductor Instantaneous power (p) - the product of v and i gives instantaneous power True Power (P true ) - ideally is zero, since all power true stored by an inductor in the positive portion of the power cycle is returned to the source during the negative portion (is shifted back and forth). If winding resistance is taken into account, the true power is: P true = (I rms ) 2 R W

33 Power curve for an inductor Reactive Thomas L. Floyd Electronics Fundamentals, 6e Electric Circuit Fundamentals, 6e Instantaneous Values Power is maximum when I and V are equal (either positive or negative) Power is zero when either I or V are zero Copyright 2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

34 Reactive Power The rate at which an inductor stores or returns power is called its reactive power (P r ), with units of VAR (volt-ampere reactive) P r = V rms I rms P r = V 2 rms/x L or P r = I 2 rmsx L

35 Quality Factor (Q) of a Coil The quality factor (Q) is the ratio of the reactive power in the inductor to the true power in the winding resistance of the coil or the resistance in series with the coil A theoretically perfect coil would have a Q of 1 Q = (reactive power) / (true power) Q = X L /R W

36 Checking a coil by measuring the resistance Troubleshooting: Coils usually open Some windings short out from time to time effecting performance Thomas L. Floyd Electronics Fundamentals, 6e Electric Circuit Fundamentals, 6e Copyright 2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

37 Basic capacitor power supply filter with a series inductor Power Supply Application Thomas L. Floyd Electronics Fundamentals, 6e Electric Circuit Fundamentals, 6e Copyright 2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

38 An inductor used as an RF choke to minimize interfering signals on the power supply line Power Supply Application Thomas L. Floyd Electronics Fundamentals, 6e Electric Circuit Fundamentals, 6e Copyright 2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

An induced emf is the negative of a changing magnetic field. Similarly, a self-induced emf would be found by

An induced emf is the negative of a changing magnetic field. Similarly, a self-induced emf would be found by This is a study guide for Exam 4. You are expected to understand and be able to answer mathematical questions on the following topics. Chapter 32 Self-Induction and Induction While a battery creates an