Alternating Current (AC) - PowerPoint Presentation

Slide1

Warm-up: Prediction AC Generator

As the ring rotates within the magnetic field, what happens?

Sketch a graph to show how the rotation of the ring will affect the reading on the attached voltmeter.Slide2

Alternating Current (AC)Read pages 439 - 454Slide3

AC generators

Video link (it’s old…and if you watch the whole thing, it’s long, but it’s good)—we’re just going to watch the first few minutes today 

https://www.youtube.com/watch?v=07uXnc1C5CA Slide4

In a nutshell…DC generators—use a split-ring

commutator to ensure that the direction of the induced emf (and resulting current) is always in the same direction upon output from the generator

AC generators—use a set of slip rings to provide constant contact with the brushes, resulting in an induced emf and current that are alternating in magnitude and in directionSlide5

Peak voltage

Flux linkage:

How is the angle in that equation related to the rotation of the coil?

(at some time, t, the angle of the coil in the magnetic field is

q

, which depends on how quickly the coil is rotating)

So…a little use of Faraday’s Law, and a little calculus later…

 Slide6

Peak Voltage

Peak Voltage

: the maximum induced

emf

that is generated by an AC generator (i.e. coil rotating in a magnetic field)

Peak VoltageSlide7

Peak Current

We are going to safely assume Ohm’s Law works, so the peak current (maximum current induced) through a resistor in an AC circuit is:

 Slide8

Power in an AC Circuit

Just like AC voltage and current, not constant with time:

Peak Power is the product of peak voltage and peak current

What would a graph of Power with respect to time look like?

 Slide9

Power is always a positive value, and will be equal to zero Watts every half rotation of the coil.Average power is ½ the peak power:Slide10

rms Voltage

Root Mean Square (rms) Voltage and Current:

The best way we have of measuring an average voltage or current in AC circuitsStep 1: Square the Current(or voltage)

Step 2: average this (now always positive) quantity

In 1 cycle, the cosine term averages to zero!

 Slide11

Step 3: Take that average’s square root

Same thing for voltage:

Average Power:

 Slide12

TransformersA tool used to take advantage of the fact that an alternating current generates an alternating magnetic flux in a coil.

An iron core connects two separate coilsPrimary coil the coil that is the “input” to the transformer

Incoming alternating current generates an ever-changing fluxSecondary coil  the coil that delivers the “output”

Because of the iron core, the flux from the primary coil induces an emf in the secondary coil and, therefore, a currentSlide13

Transformers--quantified

The induced emf in the secondary coil, as well as the amount of magnetic flux rate of change is dependent on Faraday’s Law.

The primary coil generates a magnetic flux changing at a rate shown by

The secondary coil generates an induced

emf

:

 Slide14

Transformers--continued

is a constant, which leaves us the following ratio:

Knowing that an ideal transformer will have no power loss between the coils, so

, this can also be written as:

 Slide15

Example:Slide16

Step-down and Step-up Transformers

Step-Down:A transformer designed to have a high input voltage and a low output voltageThere will be fewer loops in the secondary coil

Step-up:A transformer designed to have a low input voltage and a higher output voltageMore loops in secondary coilSlide17

A generator has a coil of wire rotating in a magnetic field. If the

rotation rate increases

, how is the

maximum output voltage

of the generator affected?

a) increases

b) decreases

c) stays the same

d) varies sinusoidally

Question 20.10

GeneratorsSlide18

The maximum voltage is the leading term that multiplies

sin

w

t

and is given by

e

0

=

NBA

w

. Therefore, if

w

increases

, then

e

0

must increase

as well.

A generator has a coil of wire rotating in a magnetic field. If the

rotation rate increases

, how is the

maximum output voltage

of the generator affected?

a) increases

b) decreases

c) stays the same

d) varies sinusoidally

Question 20.10

GeneratorsSlide19

A wire loop is in a uniform magnetic field. Current flows in the wire loop, as shown. What does the loop do?

a) moves to the right

b) moves up

c) remains motionless

d) rotates (right side away from you)

e) rotates (left side away from you)

Question 20.11

Magic LoopSlide20

There is no magnetic force on the top and bottom legs, since they are parallel to the

B

field. However, the magnetic force on the

right side

is

into the page

, and the magnetic force on the

left side

is

out of the page

. Therefore, the entire loop will tend to rotate.

a) moves to the right

b) moves up

c) remains motionless

d) rotates (right side away from you)

e) rotates (left side away from you)

A wire loop is in a uniform magnetic field. Current flows in the wire loop, as shown. What does the loop do?

This is how a motor works !!

Question 20.11

Magic LoopSlide21

TransformersA transformer has 50. turns on its primary loop and 250 turns on its secondary loop. If the input voltage is 60. VAC, what is the output voltage?Slide22

a) greater than 6 V

b) 6 V

c) less than 6 V

d) zero

A 6 V battery is connected to one side of a transformer. Compared to the voltage drop across coil A, the voltage across coil B is:

A

B

6 V

Question 20.12c

Transformers IIISlide23

The voltage across B is zero

.

Only a

changing

magnetic flux induces an emf. Batteries can provide only

dc current

.

a) greater than 6 V

b) 6 V

c) less than 6 V

d) zero

A

B

6 V

Question 20.12c

Transformers III

A 6 V battery is connected to one side of a transformer. Compared to the voltage drop across coil A, the voltage across coil B is:Slide24

Transformer Efficiency

What IS efficiency?A measure of the amount usable energy or power put out by a system as compared to the initial input of energy (power).

Reported as a percentageEfficiency of a transformer:

OR

 Slide25

How can efficiency be improved?

Laminating the core:Core made of several thin layers rather than single, solid piece of conducting material

Layers separated by thin layers of insulating material (see image on p. 445)Designed to prevent eddy currents from forming in the core material due to the internal currents created by the changing magnetic flux in the core

Layers increase resistance, lowering current in coreLower current in core reduces the rise in temperature in the core and reduces energy losses.Slide26

How can efficiency be improved?Core material

Using a material that is a “soft” magnet and can be magnetized and demagnetized easily, (i.e. iron)Wire in the coils

Low-resistance wires should be usedHigher resistance higher temperatures and heating losses (energy loss)Slide27

Transformers II

A transformer steps down an input voltage of 120. V to 5.0 V for a tablet computer. The computer requires 1.0 W of power to operate correctly.There are 2300 turns on the primary coil of the transformer.(a) How many turns are there on the secondary coil of the transformer?

(b) What is the current in the secondary coil when it is operating correctly?(c) The input current to the primary is 0.0090 A. Calculate the efficiency of the transformerSlide28

Power TransmissionPower generated at the electric plant is transformed to very high voltages

The high voltage power lines carry current long distances to a distribution stationSplit into various directions to go to communitiesStepped down to a lower voltage still to distribute to various needs: Heavy Industry (factories), light industry (small factories, large stores), or small commercial and residential, for example.

Stepped down again at your home to get to 120 VAC (±5%)PSE videoSlide29

Sample grid (taken from your textbook):Slide30

Sample:

1.8 MW of electrical power is generated by each wind turbine on a farm of 155 turbines. Assume each wind turbine is capable of generating 685 V. A transformer station is designed to step-up the voltage to 25.0 kV for local transmission lines. A second transformer is used to step-up the voltage again for long-distance transmission to 600. kV

A) What is the current in the electrical lines leading to the first transformer?B) What is the current leaving the first transformer?