22.7 The Electric Generator
THE BACK EMF GENERATED BY AN ELECTRIC MOTOR
When a motor is operating, two sources of emf are present: (1) the
applied emf V that provides current to drive the motor, and (2) the
emf induced by the generator-like action of the rotating coil.
Consistent with Lenz’s law, the induced emf (AC) acts to
oppose the applied emf and is called back emf
V −E
I=
R
(RMS or peak values)
Where peak back EMF is given by
E0 = NBAω
(like a generator!!!)
22.9 Transformers
A transformer is a device for increasing or decreasing an AC voltage.
(Does not work with DC voltage)
Secondary Coil: NS loops
Primary Coil:
NP loops
∆Φ
EP = − N P
∆t
∆Φ
ES = − N S
∆t
Same magnetic flux
contained by the iron core
Transformer
equation
ES N S
=
EP N P
or
VS N S
=
VP N P
2
22.9 Transformers
Secondary
Coil: NS loops
Primary Coil:
NP loops
“Turns Ratio” usually quoted as NS:NP
A transformer is a passive device: it cannot add energy
to the system: power input (P) = power output (S)
I PVP = I SVS
I s Vp N p
=
=
I p Vs N s
A transformer that steps up the voltage simultaneously steps
down the current, and a transformer that steps down the voltage
steps up the current.
3
Example: A 120V, 60Hz AC voltage source drives a load through transformer A with turns
ratio of 17:3 and delivers PA=85.0 W to the load. When a new transformer B is used instead,
a power of PB=340.0 W is delivered to the load. Find the turns ratio of transformer B.
ERMS = 120 V
ERMS = 120 V
A
f = 60.0 Hz
B
f = 60.0 Hz
N S : N P = 17 : 3
R
R
P = 85.0 W
P = 340.0 W
Start by finding R
NS : NP = ?
4
Example: A 120V, 60Hz AC voltage source drives a load through transformer A with turns
ratio of 17:3 and delivers PA=85.0 W to the load. When a new transformer B is used instead,
a power of PB=340.0 W is delivered to the load. Find the turns ratio of transformer B.
ERMS = 120 V
ERMS = 120 V
A
f = 60.0 Hz
B
f = 60.0 Hz
N S : N P = 17 : 3
R
R
P = 85.0 W
P = 340.0 W
NS : NP = ?
5
Example: A 120V, 60Hz AC voltage source drives a load through transformer A with turns
ratio of 17:3 and delivers PA=85.0 W to the load. When a new transformer B is used instead,
a power of PB=340.0 W is delivered to the load. Find the turns ratio of transformer B.
ERMS = 120 V
ERMS = 120 V
A
f = 60.0 Hz
f = 60.0 Hz
N S : N P = 17 : 3
VS =
R
R
P = 85.0 W
P = 340.0 W
NS : NP = ?
Start by finding R
P = I PVP = I SVS = 85.0 W
A
B
NS
17
VP = (120 V) = 680 V
3
NP
RMS values assumed for V and I
V
V
(680 V ) = 5.44 × 103 Ω
P= S →R= S =
R
P
85.0 W
2
2
2
N
3
P 85.0 W 85.0 J/s
I S = P VP = (0.708 A) = 0.125 A
=
=
= 0.708 A
NS
17
120 V 120 J/C
VP
VS
680 V
P
85.0 W
2
3
R
=
=
= 5.44 × 10 3 Ω
P = IS R → R = 2 =
=
5
.
44
×
10
Ω
or:
2
I S 0.125 A
(0.125 A)
IS
or: I P =
B
P = I PVP = I SVS = 340 W
2
(
VS )
P=
R
( N S / N P ) 2 (VP )
=
R
2
or: P = (I S )2 R = (I P ) R
(NS / N P )
2
2
IP =
VS = ( N S / N P )VP , I S = ( N S / N P ) −1 I P
PR
(NS / N P ) =
=
VP
P 340.0 W
=
= 2.83 A
VP
120 V
(340 W)(5.44 × 10 3 Ω)
= 11.3 = 34 : 3
120 V
(NS / N P ) = I P
R
5440 Ω
= (2.83 A)
= 11.3
P
340 V
6
Chapter 16
Waves and Sound
7
16.1 The Nature of Waves
Chapter 16
Waves and Sound
1. A wave is a traveling disturbance in SOME
MEDIUM
2. A wave carries energy (and possibly
information) from place to place.
8
16.1 The Nature of Waves
Example: Sesmic Waves (wave motion of the surface of the Earth)
•There are two types of waves:
1. Transverse waves ( “S” seismic waves)
Motion of a piece of the Eath is perpendicular to the direction of travel
The animation here shows a short “pulse”
http://web.ics.purdue.edu/~braile/edumod/waves/Swave.gif
9
16.1 The Nature of Waves
2. Longitudinal Wave (seismic “p” waves)
The piece of the medium marked in black moves in a
direction parallel to the direction of travel
Note in NEITHER CASE is the particle actually
transported: it simply moves about an equilibrium
point.
http://web.ics.purdue.edu/~braile/edumod/waves/Pwave.gif
10
16.1 The Nature of Waves
Water waves are partially transverse
and partially longitudinal.
IMPORTANT NOTE:
Regular waves do not transport
matter from one location to
another
TIDAL waves are NOT waves in
the physics sense…
(Tides DO transport water)
http://www.youtube.com/watch?v=7yPTa8qi5X8
11
16.2 Periodic Waves
http://web.utk.edu/~cnattras/Physics221S
pring2013/modules/m10/images/pulse.gif
The introductory example of S
(transverse) and P (longitudinal)
waves actually showed a single
wave pulse (repeatdely)
Single wave pulse
In contrast: the example of the water
wave is a periodic wave
http://web.utk.edu/~cnattras/Physics221S
pring2013/modules/m10/images/wave.gif
Periodic waves consist of cycles or
patterns that are produced over and
over again by the source.
In the lower figures, every segment of
the string vibrates in simple harmonic
Motion.
12
16.2 Periodic Waves
In the drawing, one cycle is shaded in color.
z
z
x
Picture of wave an instant in time
t
Motion of particle at a fixed location
http://www.stmary.ws/highschool/physics/home/notes/
waves/intro/Simple_harmonic_motion_animation.gif
The amplitude is the maximum excursion of a particle of the medium from
the particles undisturbed position: (usually denoted by symbol)
A
The wavelength is the length interval of one cycle of the wave: λ
The period is the time required for one complete cycle: T
The frequency is related to the period and has units of Hz, or s-1: f
1
f =
T
13
16.2 Periodic Waves
Wave Speed: v
z
T
http://upload.wikimedia.org/wikipedia/commons/
a/a8/1D_Progressive_Wave.gif
(Speed of wave propagation) =
(distance traveled by a crest in one cycle)
divided by
(time for one cycle to pass a given point)
v=
λ
T
= fλ
14
16.2 Periodic Waves
Example: A wave traveling in the positive x
direction has a frequency of 25.0 Hz, as in
the figure. Find the
(a) amplitude,
(b) wavelength,
(c) period, and
(d) speed of the wave.
15