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Inductors and Inductance: A Comprehensive Guide, Lecture notes of Electric Machines

Jordan UniversityElectric Machines

All conductors that carry a current produce a magnetic field

Typology: Lecture notes

2019/2020

Uploaded on 02/18/2020

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5. Inductors and
Inductance
1
ELECTROMAGNETIC INDUCTION
• All conductors that carry a current produce a magnetic
field
• As the magnet is moved in and out of a coil of wire in a
closed circuit an induced current will be produced
• All dynamos and generators produce electricity using
this effect
• Electromagnetic induction takes place when the
magnetic field around a conductor changes
• If the magnetic field is made to change quickly, the size
of the current induced is larger
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  1. Inductors and 1

ELECTROMAGNETIC INDUCTION

  • All conductors that carry a current produce a magnetic field
  • As the magnet is moved in and out of a coil of wire in a closed circuit an induced current will be produced
  • All dynamos and generators produce electricity using this effect
  • Electromagnetic induction takes place when the magnetic field around a conductor changes
  • If the magnetic field is made to change quickly, the size of the current induced is larger
  1. Inductors and 2

INDUCTANCE

  • Inductance is a phenomenon in which a changing current in a circuit builds up a magnetic field which induces an electromotive force either in the same circuit and opposing the current (self-inductance) or in another circuit (mutual inductance)
  • A component designed to introduce inductance into a circuit is called an inductor
  • It is usually in the form of a coil of wire
  • The energy stored in the magnetic field of the coil is proportional to its inductance and the current flowing through it
  • The magnitude of the voltage induced in a coil depends directly on the rate of change of the current through it, where L is the inductance
  • Symbol
  • Unit of inductance is the henry ( henries ) (H)

t

I

V L

  1. Inductors and 4

FUNCTION OF AN INDUCTOR (2)

  • When current starts flowing in the coil (inductor), the coil wants to build up a magnetic field
  • As the field builds up, the coil inhibits current flow
  • Once the field is built, current flows normally through the wound wire
  • When the switch is opened, the magnetic field around the coil maintains current flow in the coil until the field collapses
  • The current keeps the bulb lit for a period of time, even though the switch is open
  • In other words, an inductor can store energy in its magnetic field
  • An inductor also tends to resist any change in the amount of current flowing through it
  • Unlike capacitors, inductors impede the flow of AC signals, and allow DC signals to pass more easily
  1. Inductors and 5

VOLTAGE ACROSS AND CURRENT

THROUGH INDUCTOR EXAMPLE

  • Sketch the voltage across a 9.87mH inductor, when the current through it changes with time as shown in the graph below
  1. Inductors and 7

INDUCTORS IN CIRCUITS

  • The total equivalent inductance for series connected inductors is
  • LT = L 1 + L 2 +…+ Ln
  • For parallel connected inductors
  • 1/ LT = 1/ L 1 + 1/ L 2 +…+ 1/ Ln
  • When an inductor having no current flowing through it is first switched into a circuit, it behaves like and open circuit because the current cannot change instantaneously from its zero initial value
  • After the circuit has been switched on for a long time, the current has reached a state where its value is not changing (steady state value) anymore, hence the inductor acts as a short circuit
  • The energy stored (W) in an inductor with inductance (L) is given by
  • W = (1/2) LI^2 Joules
  1. Inductors and 8

INDUCTORS IN CIRCUITS

EXAMPLES

  • Find the initial and steady-state (final) voltage across and current through every component after the switch is closed at t = 0.
  • The inductor in the circuit below has an inductance of 0.2H, and a winding resistance of 400Ω. Find the energy stored in the inductor and the rate at which energy is dissipated by the winding under steady-state conditions.