Resource Lesson
Generators, Motors, Transformers
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Motors
The generalized equation for the operation of a motor is
Electricity + Magnetism → Motion
When electricity is supplied to a coil and it is inserted within a permanent magnetic field, the two magnetic fields repel and attract each other causing the loop to rotate. Recall the demonstration of the St. Louis motor. A DC motor is drawn as a circuit element in the following way:
The loop equation, ABCA, for this circuit would be

ε
_{motor}
 Ir +
ε
= 0
ε
_{motor}
is called the back emf of the motor and
r
is the resistance of the coil. This back emf reduced the effective voltage of the battery and is also why capacitors are used to help jump start large circuits and there is a transient voltage to motors when they are initially turned off.
Refer to the following information for the next two questions.
A particular permanentmagnet motor has a resistance of 2.0 ohms. It draws 3.0 A when operating normally on a 110 volt line.
How large is the back emf it develops?
If the motor stalls, how much current would flow through its coils?
Generators
The generalized equation for a generator is
Motion + Magnetism → Electricity
When a coil is rotated within a permanent external magnetic field, the changing flux lines generate a voltage within the coil.
Physlet: Faraday's Law of Induction
moving coil
Physlet: Generator
rotating coil
Since the coil has resistance, this induced emf will result in an induced electric current. The equation for the alternating voltage produced by the rotating coil is
v
_{instantaneous}
= V
_{o}
sin(2
π
f)t
where V
_{o}
is the coil's maximum emf which equals NBA(2
π
f) and the frequency is in rev/sec [hz]. This equation can also be expressed as
v
_{instantaneous}
= V
_{o}
sin(ωt)
where ω is the coil's angular velocity,
ω = 2
π
f.
Transformers
The Law of Transformers
states
N
_{s}
/N
_{p}
=
ε
_{s}
/
ε
_{p}
N
_{p}
and N
_{s}
are the number of loops in the primary and secondary coils.
ε
_{p}
and
ε
_{s}
are the emfs in the primary and secondary. A transformer only works when the number of flux lines through the iron core of the transformer keeps changing  therefore, the primary must be connected to an alternating source. Transformers will not operate in a DC circuit. Any change in flux in the primary is communicated to the secondary through the iron core.
The power utilized on both coils is the same since energy is conserved
. Therefore,
ε
_{p}
I
_{p}
=
ε
_{s}
I
_{s}
, which explains how electricity is transferred by the power companies. High voltages will have smaller currents and less energy loss to Joule heating. Voltages are stepped down for use in buildings at transformers. When N
_{s}
< N
_{p}
, the transformer is a "step down" transformer since the induced AC voltage of the secondary will be less than the voltage across the primary.
Related Documents
Lab:
Labs 
Telegraph Project
Resource Lesson:
RL 
A Comparison of RC and RL Circuits
RL 
A Special Case of Induction
RL 
Eddy Currents plus a Lab Simulation
RL 
Electricity and Magnetism Background
RL 
Induced Electric Fields
RL 
Induced EMF
RL 
Inductors
RL 
LC Circuit
RL 
Maxwell's Equations
RL 
Motional EMF
RL 
RL Circuits
Review:
REV 
Drill: Induction
Worksheet:
CP 
Induction
CP 
Power Transmission
CP 
Transformers
NT 
Induction Coils
WS 
Induced emf
WS 
Practice with Induced Currents (Changing Areas)
WS 
Practice with Induced Currents (Constant Area)
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