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.

RVI E−=

Consistent with Lenz’s law, the induced emf (AC) acts to oppose the applied emf and is called back emf

ωNBA=0EWhere peak back EMF is given by

(like a generator!!!) (RMS or peak values)

22.9 Transformers

A transformer is a device for increasing or decreasing an AC voltage. (Does not work with DC voltage)

tN

∆∆Φ

−= PPE

2

tN

∆∆Φ

−= SSE

Primary Coil: NP loops

Secondary Coil: NS loops

Same magnetic flux contained by the iron core

P

S

P

S

NN

=EE

P

S

P

S

NN

VV

=or Transformer equation

22.9 Transformers

s

p

s

p

p

s

NN

VV

II

==

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

Primary Coil: NP loops

Secondary Coil: NS loops

A transformer is a passive device: it cannot add energy to the system: power input (P) = power output (S)

SSPP VIVI =

“Turns Ratio” usually quoted as 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.

A Hz0.60

V 120RMS=

=fE

R

3:17: =PS NN

W 0.85=P

B Hz0.60

V 120RMS=

=fE

R

?: =PS NN

W 0.340=P

Start by finding R

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.

A Hz0.60

V 120RMS=

=fE

R

3:17: =PS NN

W 0.85=P

B Hz0.60

V 120RMS=

=fE

R

?: =PS NN

W 0.340=P

6

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.

A Hz0.60

V 120RMS=

=fE

R

3:17: =PS NN

W 0.85=P

B Hz0.60

V 120RMS=

=fE

R

?: =PS NN

W 0.340=P

A 708.0J/C 120J/s 85.0

V 120W 85.0

PP ==== V

PI

A W 0.85SSPP === VIVIP RMS values assumed for V and I

V 680V) 120(3

17S === P

P

S VNNV

A 125.0A) 708.0(173

S === PS

P VNNI

Ω×=== 3S

S 1044.5 A 125.0

V 680IVR

B W 340SSPP === VIVIP PPSPPS INNIVNNV 1SS )/( ,)/( −==

( ) ( )R

VNNR

VP2

P2

PS2

S )/(==

( )Ω×===→= 3

22S

2S 1044.5

W 0.85V 680

PVR

RVP

or:

or:

Ω×===→= 322S

2S 1044.5 A) (0.125

W 0.85IPRRIP

3:34 3.11 V 120

)1044.5W)( 340()/(

3

PPS ==

Ω×==

VRPNN

( ) ( ) 2PS

2P2

S )/( NNRIRIP ==or: 3.11

V 340 5440A) (2.83 )/( PS =Ω

==PRINN PA 83.2V 120

W 340.0

PP === V

PI

Start by finding R

Chapter 16

Waves and Sound

7

16.1 The Nature of Waves

1. A wave is a traveling disturbance in SOME MEDIUM

2. A wave carries energy (and possibly information) from place to place.

8

Chapter 16 Waves and Sound

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”

9

http://web.ics.purdue.edu/~braile/edumod/waves/Swave.gif

http://web.ics.purdue.edu/~braile/edumod/waves/Swave.gif

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.

10

http://web.ics.purdue.edu/~braile/edumod/waves/Pwave.gif

http://web.ics.purdue.edu/~braile/edumod/waves/Pwave.gif

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)

11 http://www.youtube.com/watch?v=7yPTa8qi5X8

http://www.youtube.com/watch?v=7yPTa8qi5X8

16.2 Periodic Waves

In contrast: the example of the water wave is a periodic wave 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.

The introductory example of S (transverse) and P (longitudinal) waves actually showed a single wave pulse (repeatdely)

Single wave pulse

12

http://web.utk.edu/~cnattras/Physics221Spring2013/modules/m10/images/pulse.gif

http://web.utk.edu/~cnattras/Physics221Spring2013/modules/m10/images/wave.gif

http://web.utk.edu/~cnattras/Physics221Spring2013/modules/m10/images/pulse.gifhttp://web.utk.edu/~cnattras/Physics221Spring2013/modules/m10/images/pulse.gifhttp://web.utk.edu/~cnattras/Physics221Spring2013/modules/m10/images/wave.gifhttp://web.utk.edu/~cnattras/Physics221Spring2013/modules/m10/images/wave.gif

16.2 Periodic Waves

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 T

f 1=13

Picture of wave an instant in time Motion of particle at a fixed location

z

z

x t

In the drawing, one cycle is shaded in color.

http://www.stmary.ws/highschool/physics/home/notes/waves/intro/Simple_harmonic_motion_animation.gif

http://www.stmary.ws/highschool/physics/home/notes/waves/intro/Simple_harmonic_motion_animation.gifhttp://www.stmary.ws/highschool/physics/home/notes/waves/intro/Simple_harmonic_motion_animation.gif

16.2 Periodic Waves

λλ fT

==v

Wave Speed: v

(Speed of wave propagation) = (distance traveled by a crest in one cycle)

divided by (time for one cycle to pass a given point)

14

T z

http://upload.wikimedia.org/wikipedia/commons/a/a8/1D_Progressive_Wave.gif

http://upload.wikimedia.org/wikipedia/commons/a/a8/1D_Progressive_Wave.gifhttp://upload.wikimedia.org/wikipedia/commons/a/a8/1D_Progressive_Wave.gif

15

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.

16.2 Periodic Waves

22.7 The Electric Generator22.9 Transformers22.9 TransformersSlide Number 4Slide Number 5Slide Number 6Chapter 1616.1 The Nature of Waves16.1 The Nature of Waves16.1 The Nature of Waves16.1 The Nature of Waves16.2 Periodic Waves16.2 Periodic Waves16.2 Periodic WavesSlide Number 15