Inductance Copyright 2009 Pearson Education Inc Inductance NOTE

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Inductance Copyright © 2009 Pearson Education, Inc.

Inductance Copyright © 2009 Pearson Education, Inc.

Inductance (NOTE: “Coil” Solenoid) • Often, the induced flux must be included in a

Inductance (NOTE: “Coil” Solenoid) • Often, the induced flux must be included in a circuit analysis. When the switch is closed, a sudden change in current occurs in the coil. • This current produces a magnetic field • So, an emf and current are induced in the coil Copyright © 2009 Pearson Education, Inc.

Inductor • A coil is type of circuit element called an inductor. Many inductors

Inductor • A coil is type of circuit element called an inductor. Many inductors are constructed as small solenoids. But, almost any coil or loop will act as an inductor • Whenever the current through an inductor changes, a voltage is induced in the inductor that opposes this change • This phenomenon is called self-inductance – The current changing through a coil induces a current in the same coil – The induced current opposes the original applied current, from Lenz’s Law Copyright © 2009 Pearson Education, Inc.

Inductance of a Solenoid • Faraday’s Law can be used to find the inductance

Inductance of a Solenoid • Faraday’s Law can be used to find the inductance of a solenoid. L is the symbol for inductance • The EMF across the solenoid can be expressed in terms of the inductance L: Copyright © 2009 Pearson Education, Inc.

 • These results apply to all wire coils or loops. – The value

• These results apply to all wire coils or loops. – The value of L depends on the physical size and shape of the circuit element • The voltage drop across an inductor is • The SI unit of inductance is the Henry 1 H=1 V. s/A Copyright © 2009 Pearson Education, Inc.

Mutual Inductance • It is possible for the magnetic field of one coil to

Mutual Inductance • It is possible for the magnetic field of one coil to produce an induced current in a second coil. • The coils are connected indirectly through the magnetic flux • The effect is called mutual inductance Copyright © 2009 Pearson Education, Inc.

RL Circuit • DC circuits may contain resistors, inductors, and capacitors. • The voltage

RL Circuit • DC circuits may contain resistors, inductors, and capacitors. • The voltage source is a battery or some other source that provides a constant voltage across its output terminals. • Behavior of DC circuits with inductors – Immediately after any switch is closed or opened, the induced emfs keep the current through all inductors equal to the values they had the instant before the switch was thrown – After a switch has been closed or opened for a very long time, the induced emfs are zero Copyright © 2009 Pearson Education, Inc.

RL Circuit Example Copyright © 2009 Pearson Education, Inc.

RL Circuit Example Copyright © 2009 Pearson Education, Inc.

RL Circuit Example, Analysis • The presence of resistors and an inductor make the

RL Circuit Example, Analysis • The presence of resistors and an inductor make the circuit an RL circuit • The current starts at zero since the switch has been open for a very long time • At t = 0, the switch is closed, inducing a potential across the inductor • Just after t = 0, the current in the second loop is zero • After the switch has been closed for a long time, the voltage across the inductor is zero Copyright © 2009 Pearson Education, Inc.

Time Constant for RL Circuit • The current at time t is found by

Time Constant for RL Circuit • The current at time t is found by • τ is called the time constant of the circuit • For a single resistor in series with a single inductor, τ=L/R • The voltage is given by VL = V e-t/τ Copyright © 2009 Pearson Education, Inc.

Real Inductors • Most practical inductors are constructed by wrapping a wire coil around

Real Inductors • Most practical inductors are constructed by wrapping a wire coil around a magnetic material • Filling a coil with magnetic material greatly increases the magnetic flux through the coil and therefore increases the induced emf • The presence of magnetic material increases the inductance • Most inductors contain a magnetic material inside which produces a larger value of L in a smaller package Copyright © 2009 Pearson Education, Inc.

Energy in an Inductor • Energy is stored in the magnetic field of an

Energy in an Inductor • Energy is stored in the magnetic field of an inductor • The energy stored in an inductor is PEind = ½ L I 2 – Very similar in form to the energy stored in the electric field of a capacitor • The expression for energy can also be stated as g • In terms of the magnetic field, Copyright © 2009 Pearson Education, Inc.

 • Energy contained in the magnetic field actually exists anywhere there is a

• Energy contained in the magnetic field actually exists anywhere there is a magnetic field, not just in a solenoid – Can exist in “empty” space • The potential energy can also be expressed in terms of the energy density in the magnetic field. • This expression is similar to the energy density contained in an electric field Copyright © 2009 Pearson Education, Inc.

Bicycle Odometers • • An odometer control unit is shown A permanent magnet is

Bicycle Odometers • • An odometer control unit is shown A permanent magnet is attached to a wheel A pickup coil is mounted on the axle support When the magnet passes over the pickup coil, a pulse is generated • A computer keep tracks of the number of pulses Section 21. 7 Copyright © 2009 Pearson Education, Inc.

Ground Fault Interrupters • A ground fault interrupter (GFI) is a safety device used

Ground Fault Interrupters • A ground fault interrupter (GFI) is a safety device used in many household circuits • It uses Faraday’s Law along with an electromechanical relay • The relay uses the current through a coil to exert a force on a magnetic metal bar in a switch Section 21. 7 Copyright © 2009 Pearson Education, Inc.

GFI, cont. • During normal operation, there is zero magnetic field in the relay

GFI, cont. • During normal operation, there is zero magnetic field in the relay • If the current in the return coil is smaller, a non -zero magnetic field opens the relay switch and the current turns off Copyright © 2009 Pearson Education, Inc.

Electric Guitars • An electric guitar uses Faraday’s Law to sense the motion of

Electric Guitars • An electric guitar uses Faraday’s Law to sense the motion of the strings • The metal string passes near a pickup coil wound around a permanent magnet • As the string vibrates, it produces a changing magnetic flux • The resulting emf is sent to an amplifier and the signal can be played through speakers Section 21. 7 Copyright © 2009 Pearson Education, Inc.

Generators, Motors and Cars • Motors and generators provide examples of conservation of energy

Generators, Motors and Cars • Motors and generators provide examples of conservation of energy and the conversion of energy from one type to another • A hybrid car contains two motors and a generator • The hybrid car “recaptures” some of the energy normally converted to heat when braking and stores it in batteries • A hybrid car is a practical example of the conversion between mechanical and electrical energy Section 21. 7 Copyright © 2009 Pearson Education, Inc.

Induction from a Distance • Assume a very long solenoid is inserted at the

Induction from a Distance • Assume a very long solenoid is inserted at the center of a single loop of wire • The field from the solenoid at the outer loop is essentially zero Section 21. 8 Copyright © 2009 Pearson Education, Inc.

Induction from a Distance, cont. • The field inside the solenoid at the center

Induction from a Distance, cont. • The field inside the solenoid at the center of the loop still produces a magnetic flux through the inner portion of the loop • Energy is transferred across the empty space between the two conductors • The energy is carried from the solenoid to the outer loop by an electromagnetic wave Section 21. 8 Copyright © 2009 Pearson Education, Inc.