Chapter 20
Section 1 Electricity from
Magnetism
Objectives
• Recognize that relative motion between a conductor
and a magnetic field induces an emf in the conductor.
• Describe how the change in the number of magnetic
field lines through a circuit loop affects the magnitude
and direction of the induced electric current.
• Apply Lenz’s law and Faraday’s law of induction to
solve problems involving induced emf and current.
Chapter 20
Section 1 Electricity from
Magnetism
Electromagnetic Induction
• Electromagnetic induction is the process of
creating a current in a circuit by a changing magnetic
field.
• A change in the magnetic flux through a conductor
induces an electric current in the conductor.
• The separation of charges by the magnetic force
induces an emf.
Chapter 20
Section 1 Electricity from
Magnetism
Electromagnetic Induction in a Circuit Loop
Chapter 20
Section 1 Electricity from
Magnetism
Electromagnetic Induction, continued
• The angle between a magnetic field and a circuit
affects induction.
• A change in the number of magnetic field lines
induces a current.
Chapter 20
Section 1 Electricity from
Magnetism
Characteristics of Induced Current
• Lenz’s Law
The magnetic field of the induced current is in a
direction to produce a field that opposes the
change causing it.
• Note: the induced current does not oppose the
applied field, but rather the change in the applied
field.
Chapter 20
Section 1 Electricity from
Magnetism
Characteristics of Induced Current, continued
• The magnitude of the induced emf can be predicted
by Faraday’s law of magnetic induction.
• Faraday’s Law of Magnetic Induction
 M
emf  – N
t
average induced emf = –the number of loops in the circuit 
the time rate of change in the magnetic flux
•
The magnetic flux is given by M = ABcosq.
Chapter 20
Section 1 Electricity from
Magnetism
Sample Problem
Induced emf and Current
A coil with 25 turns of wire is wrapped around a
hollow tube with an area of 1.8 m2. Each turn has
the same area as the tube. A uniform magnetic field
is applied at a right angle to the plane of the coil. If
the field increases uniformly from 0.00 T to 0.55 T in
0.85 s, find the magnitude of the induced emf in the
coil. If the resistance in the coil is 2.5 Ω, find the
magnitude of the induced current in the coil.
Chapter 20
Section 1 Electricity from
Magnetism
Sample Problem, continued
Induced emf and Current
1. Define
Given:
∆t = 0.85 s
A = 1.8 m2
N = 25 turns
R = 2.5 Ω
Bi = 0.00 T = 0.00 V•s/m2
Bf = 0.55 T = 0.55 V•s/m2
Unknown:
emf = ?
I=?
q = 0.0º
Chapter 20
Section 1 Electricity from
Magnetism
Sample Problem, continued
Induced emf and Current
1. Define, continued
Diagram: Show the coil before and after the change
in the magnetic field.
Chapter 20
Section 1 Electricity from
Magnetism
Sample Problem, continued
Induced emf and Current
2. Plan
Choose an equation or situation. Use Faraday’s
law of magnetic induction to find the induced emf in
the coil.
  AB cosq 
 M
emf  –N
 –N
t
t
Substitute the induced emf into the definition of
resistance to determine the induced current in the
coil.
emf
I
R
Chapter 20
Section 1 Electricity from
Magnetism
Sample Problem, continued
Induced emf and Current
2. Plan, continued
Rearrange the equation to isolate the unknown.
In this example, only the magnetic field strength
changes with time. The other components (the coil
area and the angle between the magnetic field and
the coil) remain constant.
B
emf  – NA cos q
t
Chapter 20
Section 1 Electricity from
Magnetism
Sample Problem, continued
Induced emf and Current
3. Calculate
Substitute the values into the equation and
solve.

V•s  
0.55
–
0.00
2 

m


emf  –(25)(1.8 m2 )(cos0.0º ) 
 –29 V
(0.85 s)
–29 V
I
 –12 A
2.5 Ω
emf  –29 V
I  –12 A
Chapter 20
Section 1 Electricity from
Magnetism
Sample Problem, continued
Induced emf and Current
4. Evaluate
The induced emf, and therefore the induced
current, is directed through the coil so that the
magnetic field produced by the induced current
opposes the change in the applied magnetic
field. For the diagram shown on the previous
page, the induced magnetic field is directed to
the right and the current that produces it is
directed from left to right through the resistor.
Chapter 20
Section 2 Generators, Motors,
and Mutual Inductance
Objectives
• Describe how generators and motors operate.
• Explain the energy conversions that take place in
generators and motors.
• Describe how mutual induction occurs in circuits.
Chapter 20
Section 2 Generators, Motors,
and Mutual Inductance
Generators and Alternating Current
• A generator is a machine that converts mechanical
energy into electrical energy.
• Generators use induction to convert mechanical
energy into electrical energy.
• A generator produces a continuously changing emf.
Chapter 20
Section 2 Generators, Motors,
and Mutual Inductance
Induction of an emf in an AC Generator
Chapter 20
Section 2 Generators, Motors,
and Mutual Inductance
Generators and Alternating Current, continued
• Alternating current is an electric current that
changes direction at regular intervals.
• Alternating current can be converted to direct
current by using a device called a commutator to
change the direction of the current.
Chapter 20
Section 2 Generators, Motors,
and Mutual Inductance
Motors
• Motors are machines that convert electrical energy
to mechanical energy.
• Motors use an arrangement similar to that of
generators.
• Back emf is the emf induced in a motor’s coil that
tends to reduce the current in the coil of a motor.
Chapter 20
Section 2 Generators, Motors,
and Mutual Inductance
Mutual Inductance
• The ability of one circuit to induce an emf in a nearby
circuit in the presence of a changing current is called
mutual inductance.
• In terms of changing primary current, Faraday’s law
is given by the following equation, where M is the
mutual inductance:
M
I
emf  –N
 –M
t
t
Chapter 20
Section 3 AC Circuits and
Transformers
Objectives
• Distinguish between rms values and maximum
values of current and potential difference.
• Solve problems involving rms and maximum values
of current and emf for ac circuits.
• Apply the transformer equation to solve problems
involving step-up and step-down transformers.
Chapter 20
Section 3 AC Circuits and
Transformers
Effective Current
• The root-mean-square (rms) current of a circuit is
the value of alternating current that gives the same
heating effect that the corresponding value of direct
current does.
• rms Current
Irms 
Imax
2
 0.707 Imax
Chapter 20
Section 3 AC Circuits and
Transformers
Effective Current, continued
• The rms current and rms emf in an ac circuit are
important measures of the characteristics of an ac
circuit.
• Resistance influences current in an ac circuit.
Chapter 20
Section 3 AC Circuits and
Transformers
Sample Problem
rms Current and emf
A generator with a maximum output emf of 205 V is
connected to a 115 Ω resistor. Calculate the rms
potential difference. Find the rms current through the
resistor. Find the maximum ac current in the circuit.
1. Define
Given:
∆Vrms = 205 V R = 115 Ω
Unknown:
∆Vrms = ? Irms = ? Imax = ?
Chapter 20
Section 3 AC Circuits and
Transformers
Sample Problem, continued
rms Current and emf
2. Plan
Choose an equation or situation. Use the equation
for the rms potential difference to find ∆Vrms.
∆Vrms = 0.707 ∆Vmax
Rearrange the definition for resistance to calculate
Irms.
Vrms
Irms 
R
Use the equation for rms current to find Irms.
Irms = 0.707 Imax
Chapter 20
Section 3 AC Circuits and
Transformers
Sample Problem, continued
rms Current and emf
2. Plan, continued
Rearrange the equation to isolate the unknown.
Rearrange the equation relating rms current to
maximum current so that maximum current is
calculated.
Irms
Imax 
0.707
Chapter 20
Section 3 AC Circuits and
Transformers
Sample Problem, continued
rms Current and emf
3. Calculate
Substitute the values into the equation and solve.
Vrms  (0.707)(205 V)  145 V
145 V
Irms 
 1.26 A
115 Ω
1.26 A
Imax 
 1.78 A
0.707
4. Evaluate The rms values for emf and current
are a little more than two-thirds the maximum
values, as expected.
Chapter 20
Section 3 AC Circuits and
Transformers
Transformers
• A transformer is a device that increases or
decreases the emf of alternating current.
• The relationship between the input and output emf is
given by the transformer equation.
N
V2  2 V1
N1
induced emf in secondary =
 number of turns in secondary 
 number of turns in primary  applied emf in primary


Chapter 20
Section 3 AC Circuits and
Transformers
Transformers, continued
• The transformer equation assumes that no power is
lost between the primary and secondary coils.
However, real transformers are not perfectly efficient.
• Real transformers typically have efficiencies ranging
from 90% to 99%.
• The ignition coil in a gasoline engine is a transformer.
Chapter 20
Section 3 AC Circuits and
Transformers
A Step-Up Transformer in an Auto Ignition System