Download Generators and Motors

Generators and Motors
Lightning Review
Last lecture:
1. Induced voltages and induction
 Induced EMF
 Faraday’s law
 Motional EMF
Review Problem: Two very long, fixed wires cross
each other perpendicularly. They do not touch but are
close to each other, as shown. Equal currents flow in
the wires, in the directions shown. Indicate the locus of
points where the net magnetic field is zero.
0 I
2 r
  BA cos
B

E  N
t
E  Blv
Generators
 A generator is something that converts mechanical energy
to electrical energy.
 Generators and motors are two of the most important
applications of induced emf (magnetic inductance).
 Alternating Current (AC) generator
 Direct Current (DC) generator
 A motor does the opposite, it converts electrical energy to
mechanical energy.
AC Generators
 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
brushed in contact with the
slip rings
AC generator
 Compute EMF
– It is only generated
in BC and DA wires
– EMF generated in
BC and DA would
be
D
C
A
B
v sin 
v
B
EBC  ED A  Blv
E  2 Blv  2Blv sin 
– Thus, total EMF is
a 
E  2 Blv sin t  2 Bl    sin t
2 
A
as v=r=a/2
AC generator (cont)
 Generalize the result to
N loops
E  NBA sin t
where we also noticed that A=la
 Note: Emax  NBA is
reached when t=90˚ or 270˚
(loop parallel to the magnetic
field)
EMF generated by the AC generator
AC generator
 Compute EMF
– It is only generated
in BC and DA wires
– EMF generated in
BC and DA would
be EBC  ED A  Blv
D
C
A
B
v sin 
v
B
E  2 Blv  2Blv sin 
– Thus, total EMF is
a 
E  2 Blv sin t  2 Bl    sin t
2 
A
as v=r=a/2
DC generator




By a clever change to the rings and brushes
of the ac generator, we can create a dc
generator, that is, a generator where the
polarity of the emf is always positive.
The basic idea is to use a single split ring
instead of two complete rings. The split ring is
arranged so that, just as the emf is about to
change sign from positive to negative, the
brushes cross the gap, and the polarity of the
contacts is switched.
The polarity of the contacts changes in phase
with the polarity of the emf -- the two changes
essentially cancel each other out, and the emf
remains always positive.
The emf still varies sinusoidally during each
half cycle, but every half cycle is a positive
emf.
Motors
 A motor is basically a generator running in
reverse. A current is passed through the coil,
producing a torque and causing the coil to
rotate in the magnetic field. Once turning,
the coil of the motor generates a back emf,
just as does the coil of a generator. The
back emf cancels some of the applied emf,
and limits the current through the coil.
Motors and Back emf
 The phrase back emf
is used for an emf that
tends to reduce the
applied current
 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
Example: coil in magnetic field
A coil of area 0.10 m² is rotating at 60 rev/s with its axis of rotation
perpendicular to a 0.20T magnetic field. (a) If there are 1000 turns on
the coil, what is the maximum voltage induced in the coil? (b) When the
maximum induced voltage occurs, what is the orientation of the coil
with respect to the magnetic field?
Eddy currents (application)
 Magnetic Levitation (Maglev) Trains
– Induced surface (“eddy”) currents produce field in opposite direction
S
N
“eddy” current
rails
– Maglev trains today can travel up to 310 mph
 Twice the speed of Amtrak’s fastest conventional train!
– May eventually use superconducting loops to produce B-field
 No power dissipation in resistance of wires!
Self-inductance
 When a current flows through a loop, the magnetic field
created by that current has a magnetic flux through the
area of the loop.
 If the current changes, the magnetic field changes, and so
the flux changes giving rise to an induced emf. This
phenomenon is called self-induction because it si the
loop's own current, and not an external one, that gives rise
to the induced emf.
 Faraday’s law states

E  N
t
 The magnetic flux is proportional to the magnetic field,
which is proportional to the current in the circuit
 Thus, the self-induced EMF must be proportional to the
time rate of change of the current
I
E  L
t
where L is called the inductance of the device
 Units: SI: henry (H)
 If flux is initially zero,
1 H  1V  s
A
 N 
LN

I
I
Example: solenoid
A solenoid of radius 2.5cm has 400 turns and a length of 20 cm. Find
(a) its inductance and (b) the rate at which current must change
through it to produce an emf of 75mV.