Induced Voltages And Inductance

1
Induced Voltages And Inductance

• Chapter 20
• Hans Christian Oersted

2
Introduction

• Oersteds discovery was the first evidence of a
  link between electricity and magnetism.

3
Symmetry in Physics

• Symmetry in nature helps scientists to make new
  discoveries.

4
Generating Electricity

• Could magnetic fields produce electric currents?
• Joseph Henry made this discovery
• Power plants were the result of his efforts

5
Induced emf And Magnetic Flux

• Faradays experiment
• A current can be produced by a changing magnetic
  field.
• 20.1

6
Primary and Secondary Coils

• A steady magnetic field in the primary coil
  cannot produce a current in the secondary coil.

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Induced emf And Magnetic Flux

• Magnetic flux (F)
• The flux is proportional to the number of lines
  passing through the loop
• Changes in the flux induce a change in the emf.
• 20.2

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Magnetic Flux Formula

• ?q is the angle between the B field and
• the normal to the plane of the loop

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Faradays Law of Induction

• A simple demonstration
• Wire loop, galvanometer, magnet
• 20.4

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Induced Current

• A current is set up in the loop as long as there
  is relative motion between the magnetic field and
  the loop.
• This is an induced current.
• 20.4

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Faradays Law of Induction

• The induced emf (e) in a circuit equals the rate
  of change of the magnetic flux through the
  circuit.

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• Formula for Faradays Law of magnetic induction

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Faradays Law of Induction

• Since F B.A.cosq
• And e -N.DF/Dt
• Then e -N.D (B.A.cosq) /Dt

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Lenzs Law

• The induced current tries to maintain the
  original flux through the circuit.
• It sets up a magnetic field that opposes any
  change in the original magnetic field.

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Applications of Faradays Law

• Electric guitar
• Metal strings
• Pickup coil
• Cruise control
• Ground fault interrupter (GFI)
• Protects against electrical shock
• Where is it used?
• How does it work?
• SIDS monitor
• 20.10a, 209, 20.8, 214, 20.5

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Motional emf

• Motional emf is the emf induced in a conductor
  moving through a magnetic field.
• Example A straight conductor moving through a
  magnetic field
• 20.8, 20.13

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• Formula

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Motional emf

• A potential difference (DV) is maintained across
  a conductor as long as there is motion through
  the field.
• If the direction of the motion is reversed, the
  polarity also reverses.

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Motional emf

• Motion involving a closed conducting path
• Current flows through the circuit
• 162, 211

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• Important Formulas

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Lenzs Law Revisited

• Another example (Figure 20.17)
• A stationary conducting loop and a bar magnet
• 215, 20.13, 165

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Applications of Magnetic Induction

• Cassette tape recorders/players
• Magnetic tape
• Recording head
• Playback head
• VHS recorders/players
• Computer hard drives

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Questions

• 1 - 7
• Pg. 689

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AC Generators

• The alternating current (ac) generator
• Converts mechanical energy to electrical energy
• Has a coil rotating in a magnetic field
• Slip rings
• Insure that the output voltage changes polarity
• Stationary brushes
• 20.20, 216

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Types of Commercial Power Plants

• Fossil Fuel
• Hydroelectric
• Nuclear

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Total emf

• Formula for total emf
• Note wt q and w 2pf (f 60 Hz in
  USA)
• q is measured between the magnetic field and
  the normal to the loop.
• Maximum emf occurs when the plane of the loop is
  parallel to the magnetic field
• 213

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DC Generators

• The direct current (dc) generator
• Uses a split ring or commutator
• This insures that the output voltage does not
  change polarity.
• 20.22

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Motors and Back emf

• A motor is the opposite of a generator.
• Because of Lenzs Law, back emf is generated in a
  motor.
• Back emf increases with rotational speed.
• Back emf tends to reduce current flow in the
  windings.
• Maximum current is present when the motor starts
  up.
• 217

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Back emf vs. Speed
31

• Equation for back emf

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Eddy Currents

• Eddy currents are circular currents which occur
  in a piece of metal when it moves through a
  magnetic field

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Magnetic Damping

• The magnetic fields produced by the eddy currents
  try to prevent motion of the metal through the
  field.

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Effects of Eddy Currents

• The effects of eddy currents are undesirable in
  motors and generators.
• These effects can be reduced
• Laminations are used

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Laminations in an Armature
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Self-Inductance

• A changing flux through the circuit arises from
  the circuit itself.
• This occurs in coils and solenoids
• Solenoid Video

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Self-Induced emf

• The self induced emf is proportional to the time
  rate of change of current
• L is a constant representing the inductance of
  the device and is measured in Henries (H).

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Inductance

• Formula for inductance (L)

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Inductors

• An inductor is a circuit element which is used to
  provide inductance.
• Usually a closely wrapped coil of many turns
  

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Inductance

• Inductance (L) is a measure of the opposition to
  the rate of change of current.
• Schematic symbol
• 20.27/20.28

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RL Circuits

• RL time constant (t)
• The time that it takes for the current in the
  circuit to reach 63.2 of its maximum value.

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Energy Stored In A Magnetic Field

• Current flowing through a solenoid produces a
  magnetic field.
• The battery must do work to produce a current in
  a coil.
• This energy is stored in the magnetic field of
  the coil.
• 37-1, 14, 78

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Questions

• 8,10, 11, 13, 14
• Pg. 689