Transcript Generators and Motors

Generators and Motors
AP Physics C
Montwood High School
R. Casao
 Generators and motors
are important devices that
operate on the principle of
electromagnetic
induction.
 Consider the alternating
current (AC) generator, a
device that converts
mechanical energy to
electrical energy.
 In simple form, the AC
generator consists of a
loop of wire rotated by
some external means in a
magnetic field.
 In commercial power plants, the energy required to rotate the loop
can be derived from a variety of sources:
 falling water directed onto turbine blades to produce rotary motion in a
hydroelectric plant;
 heat produced by burning coal converts water to steam which is
directed against turbine blades to produce rotary motion in a coal-fired
plant.
 As the loop rotates, the magnetic flux thru the loop changes with
time, inducing an EMF and a current in an 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.
 Suppose that the AC generator loop has N turns, all of the same area
A, and rotates with constant angular velocity ω.
 If  is the angle between the magnetic field B and the normal to the
plane of the loop (the area vector A), then the magnetic flux thru
the loop at any time t is: Φm = B·A·cos  = B·A·cos (ω·t), where
 = ω·t and the clock is set so that t = 0 s when  = 0 rad.
 The induced EMF in the coil is:
dΦm
EMF =  N 
dt
d(B  A  cos  ω  t )
EMF =  N 
dt
d(cos  ω  t )
EMF =  N  B  A 
dt
d(ω  t)
EMF =  N  B  A   sin  ω  t  
dt
dt
EMF = N  B  A  sin  ω  t   ω 
dt
EMF = N  B  A  ω  sin  ω  t 
 The EMF varies sinusoidally with time.
 The maximum EMF occurs when sin (ω·t) = 1 and has the value
EMFmax = N·B·A·ω. This occurs when the angle  = ω·t between
the magnetic field B and the area vector A is 90º and 270º.
 EMF = EMFmax when the magnetic field is in the plane of the coil
and the time rate of change of magnetic flux is a maximum.
 EMF = 0 V when the angle  = ω·t between the magnetic field B
and the area vector A is 0º and 180º. This occurs when the
magnetic field vector is perpendicular to the plane of the coil and
the time rate of change of magnetic flux is zero.
 The frequency (ω = 2·π·f) for commercial generators in the US and
Canada is 60 Hz; some European countries use 50 Hz.
EMF Induced in a Generator
 An AC generator consists of 8 turns of wire of area 0.09 m2 and
total resistance 12 . The loop rotates in a magnetic field of 0.5 T
at a constant frequency of 60 Hz.
 What is the maximum induced EMF?
  2    f  2    60 Hz  377 Hz
EMFmax  N  B  A  
2
EMFmax  8  0.5 T  0.9 m  377 Hz
EMFmax  136V
 What is the maximum induced current?
EMFmax 136V
I 

 11.3 A
R
12 
 Determine the time variation of the induced EMF and the induced
current when the output terminals are connected by a lowresistance conductor.
EMF  N  B  A    sin   t   EMFmax  sin   t 
EMF  136V  sin  377 Hz  t 
I  Imax  sin   t 
I  11.3 A  sin  377 Hz  t 
 The direct current (DC) generator is used to charge storage
batteries in older cars.
 The components are essentially the same as those of the ac
generator, except that the contacts to the rotating loop are made
using a split ring, or commutator.
 The output voltage always has
the same polarity and the
current is a pulsating direct
current.
 The reason for the pulsating direct current occurs because the




contacts to the split ring reverse their roles every half cycle.
At the same time, the polarity of the induced EMF reverses; so the
polarity of the split ring (which is the same as the polarity of the
output voltage) remains the same.
A pulsating DC current is not suitable for most applications.
To obtain a more steady DC current, commercial DC generators use
many armature coils and commutators distributed so that the
sinusoidal pulses from the various coils are out of phase.
When the pulses are superimposed, the DC output is almost free of
fluctuations.
Motors
 Motors are devices that convert electrical energy into mechanical
energy.
 A motor is a generator operating in reverse.
 Instead of generating a current by rotating a loop, a current is
supplied to the loop by a battery and the torque acting on the
current-carrying loop causes it to rotate.
 Useful mechanical work can be done by attaching the rotating
armature to some external device.
 As the loop rotates, the changing magnetic flux induces an EMF in
the loop.
 The induced EMF always acts to reduce the current in the loop; if
not, Lenz’s law would be violated.
 The back EMF increases in magnitude as the rotational speed of
the armature increases.
 The back EMF is an EMF that tends to reduce the supplied
current.
 Since the voltage available to supply current equals the difference
between the supply voltage and the back EMF, the current thru
the armature coil is limited by the back EMF.
 When a motor is first turned on, there is initially no back EMF and
the current is very large because it is limited only by the resistanc of
the coil.
 As the coils begin to rotate, the induced back EMF opposes the
applied voltage and the current in the coils is reduced.
 If the mechanical load increases, the motor will slow down, which
causes the back EMF to decrease.
 The reduction in the back EMF increases the current in the coils
and therefore increases the power needed from the external
voltage source.
 For this reason, the power requirements are greater for starting a
motor and for running it under heavy loads.
 If the motor is allowed to run under no mechanical load, the back
EMF reduces the current to a value just large enough to overcome
losses due to heat and friction.
 If a very heavy load jams the motor so that it cannot rotate, the
lack of a back EMF can lead to dangerously high current in the
motor’s wires.
The Induced Current in a Motor
 Assume that a motor having coils with a resistance of 10  is
supplied by a voltage of 120 V. When the motor is running at
its maximum speed, the back EMF is 70 V.
 Find the current in the coils when the motor is first turned on.
 When the motor is first turned on, the back EMF is 0 V.
 The current in the coils is maximum and equal to:
EMF 120V
I 

 12 A
R
10 
 Find the current in the coils when the motor has reached maximum
speed.
 At the maximum speed, the back EMF has its maximum value.
 The effective supply voltage is now the external source minus the
back EMF.
 The current is reduced to:
EMF  EMFback 120V  70V
I 

 5A
R
10 
 Suppose that the motor is in a circular saw. You are operating the
saw and the blade becomes jammed in a piece of wood so that the
motor cannot turn. By what percentage does the power input to the
motor increase when it is jammed?
 The reason an object with a motor can become warm when the
motor is prevented from turning is due to the increased power
input to the motor.
 The higher rate of energy transfer results in an increase in the
internal energy of the coil, which is undesirable.
 When the motor is jammed, the current is 12 A; when the motor
is free to turn, the current is 5A.
Pjammed
Pnot jammed

I 2 jammed  R
I 2not jammed
R

I 2 jammed
I 2not jammed
12 A 

2
5 A 
2
 5.76
 Pjammed = 5.76·Pnot jammed; this represents a 476% increase in the
input power.
 The high power input when the motor is jammed can cause the coil
to heat up to the point where it is permanently damaged.