CollegePhysics B

Transformers

Electro-magnetism

College Physics B - PHY2054C

Transformers & Electromagnetic Waves

10/08/2014

My Office Hours:

Tuesday 10:00 AM - Noon

206 Keen Building

CollegePhysics B

Transformers

Electro-magnetism

PHY2054C

Second Mini-Exam next week on Wednesday!!

• Location: UPL 101, 10:10 - 11:00 AM

• Exam on chapters 22, 23 & 25 (HW 5, 6, 7 & 8)

• Magnetic forces & fields (right-hand rules)

• Induction, Faraday’s Law, Lenz’s Law

• Generator & Transformers

• Eletromagnetic Spectrum & Waves

• Equation sheet will be provided.

• Do not forget to bring your student ID!

CollegePhysics B

Transformers

Electro-magnetism

Review Question 1

The three loops of wire shown in the figure are all subject to

the same uniform magnetic field that does not vary with time.

Loop 1 oscillates back and forth as the bob in a pendulum,

loop 2 rotates about a vertical axis, and loop 3 oscillates up

and down at the end of a spring.

Which loop, or loops, will have an induced emf?

A Loop 1

B Loop 2

C Loop 3

D Loops 1 and 3

E Loops 2 and 3

CollegePhysics B

Transformers

Electro-magnetism

Review Question 1

The three loops of wire shown in the figure are all subject to

the same uniform magnetic field that does not vary with time.

Loop 1 oscillates back and forth as the bob in a pendulum,

loop 2 rotates about a vertical axis, and loop 3 oscillates up

and down at the end of a spring.

Which loop, or loops, will have an induced emf?

A Loop 1

B Loop 2

C Loop 3

D Loops 1 and 3

E Loops 2 and 3

CollegePhysics B

Transformers

Electro-magnetism

Review Question 2

The two identical bar magnets in the figure are dropped from

rest along a vertical line passing through the center of the

rings, as shown. The two rings are identical in every respect

except that the ring on the right has a small break in it. Calling

aL and aR the magnitude of the downward accelerations of the

magnets on the left and right, respectively, you observe that

A It is not possible to predict the outcome of this

experiment with the data given.

B aL = aR.

C aL > aR.

D aL < aR.

CollegePhysics B

Transformers

Electro-magnetism

Review Question 2

The two identical bar magnets in the figure are dropped from

rest along a vertical line passing through the center of the

rings, as shown. The two rings are identical in every respect

except that the ring on the right has a small break in it. Calling

aL and aR the magnitude of the downward accelerations of the

magnets on the left and right, respectively, you observe that

A It is not possible to predict the outcome of this

experiment with the data given.

B aL = aR.

C aL > aR.

D aL < aR.

CollegePhysics B

Transformers

Electro-magnetism

Review Question 3

The wire in the figure carries a current I that is increasing with

time at a constant rate. The induced emf in each of the loops

is such that

A loop A has clockwise emf, loop B has no induced emf,

and loop C has counterclockwise emf.

B loop A has counterclockwise emf, loop B has no induced

emf, and loop C has clockwise emf.

C loop A has counterclockwise emf, loop B clockwise emf,

and loop C has clockwise emf.

D all loops experience

counterclockwise emf.

E no emf is induced in

any loop.

CollegePhysics B

Transformers

Electro-magnetism

Review Question 3

The wire in the figure carries a current I that is increasing with

time at a constant rate. The induced emf in each of the loops

is such that

A loop A has clockwise emf, loop B has no induced emf,

and loop C has counterclockwise emf.

B loop A has counterclockwise emf, loop B has no induced

emf, and loop C has clockwise emf.

C loop A has counterclockwise emf, loop B clockwise emf,

and loop C has clockwise emf.

D all loops experience

counterclockwise emf.

E no emf is induced in

any loop.

CollegePhysics B

Transformers

Electro-magnetism

Outline

1 Transformers

2 Electromagnetism

CollegePhysics B

Transformers

Electro-magnetism

Transformers

Transformers are devices that can increase or decrease the

amplitude of an applied AC voltage:

• A simple transformer consists of two solenoid coils with

the loops arranged such that all or most of the magnetic

field lines and flux generated by one coil passes through

the other coil.

CollegePhysics B

Transformers

Electro-magnetism

Transformers

Transformers are devices that can increase or decrease the

amplitude of an applied AC voltage:

1 An AC current in one coil will induce an AC voltage

across the other coil.

2 An AC voltage source is typically attached to one of the

coils called the input coil.

3 The other coil is called the output coil.

CollegePhysics B

Transformers

Electro-magnetism

Transformers

Faraday’s Law applies to both coils:

Vin =Φin

∆tand Vout =

Φout

∆t

If the input coil has N in turns and the output coil has N out turns,

the flux in the coils is related by:

Φout =N out

N in

Φin

Vout =N out

N in

Vin

Transformers cannot

change DC voltages!

CollegePhysics B

Transformers

Electro-magnetism

Transformers

Most practical transformers have central regions filled with a

magnetic material. This produces a larger flux, resulting in a

larger voltage at both the input and output coils. However:

Vout

Vin

= constant

Φout =N out

N in

Φin

Vout =N out

N in

Vin

Transformers cannot

change DC voltages!

CollegePhysics B

Transformers

Electro-magnetism

Transformers

At the power plant

Supply voltage of about 5 000 V

Cross-country lines

Voltage of about 500 000 V

CollegePhysics B

Transformers

Electro-magnetism

Transformers and Power

Transformers are used in the transmission of electric power

over long distances:

• Many household appliances use transformers to convert

the AC voltage at a wall socket to the smaller voltages

needed in many devices.

• The output voltage of a transformer can also be made

much larger by arranging the number of coils.

According to the principle of energy conservation, the energy

delivered through the input coil must either be stored in the

transformer’s magnetic field or transferred to the output circuit:

• The power delivered to the input coil must equal the

output power.

CollegePhysics B

Transformers

Electro-magnetism

Transformers and Power

According to the principle of energy conservation, the energy

delivered through the input coil must either be stored in the

transformer’s magnetic field or transferred to the output circuit:

• Since P = V I, if Vout is greater than Vin, then I out must be

smaller than I in.

• Pin = Pout only in ideal transformers

In real transformers, the coils always have a small

electrical resistance causing some power dissipation.

For a real transformer, the output power is always

less than the input power.

• Power carried by the power line:

Pavg = Vrms I rms

CollegePhysics B

Transformers

Electro-magnetism

Example

An AC power line operates with a voltage Vrms = 500, 000 V

and carries an AC current with I rms = 1000 A.

What is the average (rms) power carried by the power line?

Pavg = Vrms I rms = (500, 000 V) (1000 A) = 500 MW

CollegePhysics B

Transformers

Electro-magnetism

Example

An AC power line operates with a voltage Vrms = 500, 000 V

and carries an AC current with I rms = 1000 A.

What is the average (rms) power carried by the power line?

Pavg = Vrms I rms = (500, 000 V) (1000 A) = 500 MW

If 10 % of the power is dissipated in the power line itself, what

is the resistance of the power line?

P line = I2rms R line = (0.10)Pavg

R line =(0.10)Pavg

I 2rms

=(0.10) (5 × 108 W)

(1000 A)2= 50 Ω

CollegePhysics B

Transformers

Electro-magnetism

Example

An AC power line operates with a voltage Vrms = 500, 000 V

and carries an AC current with I rms = 1000 A.

The same power line is now operated with a reduced voltage

of Vrms = 250, 000 V and current I rms = 2000 A. The product

Vrms I rms is still the same, so the power carried by the line is the

same. What percentage of this power is now dissipated in the

power line?

P line = I2rms R line = (2000 A)2 (50 Ω) = 2.0 × 108 W

The percentage of the total power now dissipated in the line is:

Pline

Ptotal

× 100 =2.0 × 108 W

5.0 × 108 W× 100 = 40 %

compared to the initial 10 %.

CollegePhysics B

Transformers

Electro-magnetism

Outline

1 Transformers

2 Electromagnetism

CollegePhysics B

Transformers

Electro-magnetism

Connection between Electricity

and Magnetism

Sources of Electric Fields Sources of Magnetic Fields

Electric Charge

CollegePhysics B

Transformers

Electro-magnetism

Electric Fields

Michael Faraday

(1791 - 1867)

Capacitor

Static Point Charges

CollegePhysics B

Transformers

Electro-magnetism

Connection between Electricity

and Magnetism

Sources of Electric Fields Sources of Magnetic Fields

Electric Charge Moving Electric Charge

CollegePhysics B

Transformers

Electro-magnetism

Electromagnetism

Christian Oersted

(1777 - 1851)

Field around a current-carrying wire is fairly weak

CollegePhysics B

Transformers

Electro-magnetism

Connection between Electricity

and Magnetism

Sources of Electric Fields Sources of Magnetic Fields

Electric Charge Moving Electric Charge

Changing Magnetic Fields

CollegePhysics B

Transformers

Electro-magnetism

Transformer

• Alternating current in one circuit induces analternating current in a second circuit.

• Transfers power between the two circuits.

• Doesn’t transfer charge between the two circuits.

CollegePhysics B

Transformers

Electro-magnetism

Connection between Electricity

and Magnetism

Sources of Electric Field Sources of Magnetic Fields

Electric Charge Moving Electric Charge

Changing Magnetic Fields Changing Electric Fields

CollegePhysics B

Transformers

Electro-magnetism

Connection between Electricity

and Magnetism

Sources of Electric Field Sources of Magnetic Fields

Electric Charge Moving Electric Charge

Changing Magnetic Fields Changing Electric Fields

Electric fields that change with time producemagnetic fields.

⇒ Electromagnetic Waves

CollegePhysics B

Transformers

Electro-magnetism

James Clerk Maxwell

Scottish Physicist

(1831 - 1879)

CollegePhysics B

Transformers

Electro-magnetism

James Clerk Maxwell

Can these fields havea life on their own?

Can they propagateindependently of thecharges?

Scottish Physicist

(1831 - 1879)

CollegePhysics B

Transformers

Electro-magnetism

James Clerk Maxwell

Can these fields havea life on their own?

Can they propagateindependently of thecharges?

Maxwell formulateda complete theory onelectromagnetism.

Also predictedelectromagneticwaves

CollegePhysics B

Transformers

Electro-magnetism

Experimental Evidence of

Electromagnetic Waves

Heinrich Hertz

German Physicist

(1857 - 1894)

1 What is the nature of electric and magnetic fields?

2 What is the idea of action at a distance?

3 How fast do the field lines associated with a charge react

to a movement in the charge?

CollegePhysics B

Transformers

Electro-magnetism

The History of Wireless Communication

1865 Prediction of radio waves (James Clerk Maxwell)

1886 Experimental evidence of radio waves

(Heinrich Hertz)

1895 Signal transmission over 10 m

1899 Signal transmission over the English Channel

(Giulielmo Marconi)

1901 Signal transmission over the Atlantic Ocean

CollegePhysics B

Transformers

Electro-magnetism

The History of Wireless Communication

1865 Prediction of radio waves (James Clerk Maxwell)

1886 Experimental evidence of radio waves

(Heinrich Hertz)

1895 Signal transmission over 10 m

1899 Signal transmission over the English Channel

(Giulielmo Marconi)

1901 Signal transmission over the Atlantic Ocean