Transcript 20.5 Generators  Alternating Current (AC) generator  Converts mechanical energy to electrical energy  Consists of a wire loop rotated by some external means 

20.5 Generators

Alternating Current (AC) generator
 Converts mechanical energy to electrical energy
 Consists of a wire loop rotated by some external
means
 There are a variety of sources that can supply
the energy to rotate the loop
 For example, these may include falling water
or heat by burning coal to produce steam
AC Generators, cont.

Basic operation of the generator
 As the loop rotates, the
magnetic flux through it
changes with time
 This induces an emf and a
current in the external circuit
 The ends of the loop are
connected to slip rings that
rotate with the loop
 Connections to the external
circuit are made by stationary
brushes in contact with the
slip rings
AC Generators, cont.
Area A=ℓa
The emf generated in wire BC is Bℓv where ℓ is the
length of the wire and v is the velocity component
perpendicular to the B field (v has no effect on the
charges in the wire ). An emf of Bℓv is also generated
in the wire DA with the same sense as in BC. Because
v=v sinq, the total emf is ε =2Bℓv sinθ.
AC Generators, cont.
Since v=rw (tangential speed=radius
times angular speed), it follows v=(a/2)w
and
wt
ε = 2Bℓv sinθ = 2Bℓ (a/2)w sinθ
Therefore, e=Bℓaw sinwt and with A=ℓa
e=NBAw sinwt
For a coil with N
turns
Generator equation from
Faraday’s law
wt
e=-NDB/Dt
e=-NBA[D(cosq)/Dt]
Consider: d(coswt)/dt=-wsinwt
e=NBAwsinwt
emax = NBAw (maximum value of the emf)
e=emaxsinwt=emaxsin2ft
2f
AC Generators, final

The emf generated by the
rotating loop can be found
by
ε =2Bℓv=2Bℓv sinθ
If the loop rotates with a
constant angular speed, ω,
and N turns
ε=NBAω sinωt
 ε = εmax when loop is
parallel to the field
 ε = 0 when when the loop
is perpendicular to the field

Direct current (DC) Generators
Components are
essentially the same
as that of an ac
generator
 The major difference
is the contacts to
the rotating loop are
made by a split ring,
or commutator

DC Generators, cont
The output voltage always
has the same polarity
 The current is a pulsating
current
 To produce a steady
current, many loops and
commutators around the
axis of rotation are used
 The multiple outputs
are superimposed and
the output is almost
free of fluctuations

Motors
Motors are devices that convert
electrical energy into mechanical energy
 A motor is a generator run in reverse
 A motor can perform useful mechanical
work when a shaft connected to its
rotating coil is attached to some
external device

Motors and Back emf
Back emf
The applied voltage V supplies the current I to
drive the motor. The circuit shows V along with
the electrical equivalent of the motor, including
the resistance R of its coil and the back emf e.
Motors and Back emf
The phrase back emf is used for an emf that tends
to reduce the current due to an applied voltage 
current through the motor: I=V-eb/R, where V is
the line voltage, eb is the back emf and R is the
coil resistance
 When a motor is turned on, there is no back emf
initially
 The current is very large because it is limited only
by the resistance of the coil

Motors and Back emf, cont.
As the coil begins to rotate, the induced
back emf opposes the applied voltage
 The current in the coil is reduced
 The power (i.e., current) requirements
for starting a motor and for running it
under heavy loads are greater than
those for running the motor under
average loads

Example: A motor has a 10  coil. When running at its
maximum speed, the back emf is 70 V. Find the current
(a) when the motor starts and (b) when the motor has
reached its maximum speed.
(a) I=V/R=120 V/10 
 I=12 A

(b) I=(V-eb)/R
 I=(120 V-70 V)/10 
 I=50 V/10 =5 A

20.6 Self-inductance

Self-inductance occurs when the changing
flux through a circuit arises from the circuit
itself




As the current increases, the magnetic flux
through a loop due to this current also increases
The increasing flux induces an emf that opposes
the current
As the magnitude of the current increases, the
rate of increase lessens and hence the induced
emf decreases
This opposing emf results in a gradual increase in
the current
Self-inductance, cont.
(a) A current in the coil produces a magnetic field
directed to the left. (b) If the current increases, the
coil acts as a source of emf directed as shown by
the dashed battery. (c) The induced emf in the coil
changes its polarity if the current decreases.
Self-inductance, cont.

The self-induced emf is given by Faraday’s
law and must be proportional to the time rate
of change of the current
D B
DI
e = N
= L
Dt
Dt


L is a proportionality constant called the
inductance of the device
The negative sign indicates that a changing
current induces an emf in opposition to
that change
Self-inductance, final
The inductance of a coil depends on
geometric factors
 The SI unit of self-inductance is the

Henry


1 H = 1 (Vs)/A
The equation for L
DΦB
L=N
DI
20.7 RL Circuits
Inductor has a large inductance (L) and consist
of closely wrapped coil of many turns
 Inductance can be interpreted as a measure of
opposition to the rate of change in the current



Remember resistance R is a measure of opposition
to the current
As a circuit is completed, the current begins to
increase, but the inductor produces an emf that
opposes the increasing current

Therefore, the current doesn’t change from 0 to its
maximum instantaneously
Comparison of R and L in a
simple circuit
e=-IR
R is a measure of opposition
to the current
e=-L(DI/Dt)
L is a measure of opposition to
the rate of change in current
RL Circuit
When the current
reaches its maximum,
the rate of change and
the back emf are zero
 The time constant, , for
an RL circuit is the time
required for the current
in the circuit to reach
63.2% of its final value

RL Circuit, cont

The time constant depends on R and L
L
=
R

The current at any time can be found
by
I=

1 e 
R
e
t/
QUICK QUIZ 20.5
The switch in the circuit shown in the figure below is closed and the lightbulb
glows steadily. The inductor is a simple air-core solenoid. An iron rod is inserted
into the interior of the solenoid, which increases the magnitude of the magnetic
field in the solenoid. As the rod is inserted into the solenoid, the brightness of the
lightbulb (a) increases, (b) decreases,
or (c) remains the same.
20.8 Energy Stored in a
Magnetic Field
 The
emf induced by an inductor prevents
a battery from establishing an
instantaneous current in a circuit
 The battery has to do work to produce a
current
 This work can be thought of as energy
stored by the inductor in its magnetic
field
Energy stored, final
 The
increment of work done by a battery to
move DQ through an inductor is: DW=DQe
 DW=DQ [L(DI/Dt)]
 Since I=DQ/Dt, the work done is:
DW=LI (DI)
Energy stored by
an inductor

1 2
W = L IdI = LI
2