Generators

• Textbook Sections 23-6 – 23-10

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Physics 1161: Lecture 16

Review: Two uses of RHR’s

• Force on moving charge in Magnetic field – Thumb: v (or I)– Fingers: B – Palm: F on + charge

• Magnetic field produced by moving charges – Thumb: I (or v for + charges)

– Fingers: curl along B field

Palm: out of page.

BI

F

+ v+ + +

I

Review: Induction• Lenz’s Law

– If the magnetic flux (B) through a loop changes, an EMF will be created in the loop to oppose the change in flux

– EMF current (V=IR) additional B-field.• Flux decreasing => B-field in same direction as original

• Flux increasing => B-field in opposite direction of original

• Faraday’s Law– Magnitude of induced EMF given by:

if

if

ttt

Review: Rotation Variablesv, , f, T

• Velocity (v):– How fast a point moves. – Units: usually m/s

• Angular Frequency ():– How fast something rotates. – Units: radians / sec

r

vv

v = r

f = / 2

T = 1 / f = 2 /

• Frequency ( f ):– How fast something rotates.– Units: rotations / sec = Hz

• Period (T):– How much time one full rotation takes.– Units: usually seconds

Generators and EMF

rL = A

side 1 = r B L sin()

side 2 = r B L sin()

loop = side 1 + side 2

2r B L sin()

loop = A B sin()

loop = A B sin(t)

vv

•

x

r

1

2

t

AB

AB

EMF is voltage!

side 1 = v B L sin()v = r

At which time does the loop have the greatest emf (greatest / t)?

1 2 3

32%

43%

25%

1. 12. 23. 3

At which time does the loop have the greatest emf (greatest / t)?

1 2 3

26%

60%

14%

1. 12. 23. 3

1) Has greatest flux, but = 0 so = 0.

2) (Preflight example) 30 so AB/2.

3) Flux is zero, but = 90 so = AB.

Comparison:Flux vs. EMF

Flux is maximum– Most lines thru loop

EMF is minimum– Just before: lines enter from left– Just after: lines enter from left– No change!

Flux is minimum – Zero lines thru loop

EMF is maximum – Just before: lines enter from top. – Just after: lines enter from bottom.– Big change!

•

x

•x

Preflights 16.1, 16.2, 16.3

vv

•

x

r

Flux is _________ at moment shown.

Increasing

decreasing

not changing

When =30°, the EMF around the loop is:

increasing

decreasing

not changing

EMF is increasing!

Preflights 16.1, 16.2, 16.3

vv

•

x

r

Flux is decreasing at moment shown.

When =30°, the EMF around the loop is:

increasing

decreasing

not changingEMF is increasing!

Generators and Torque

vv

•

x

r

= A B sin()

Recall:

= A B I sin()

= A2 B2 sin2()/RTorque, due to current and B field, tries to slowspinning loop down. Must supply external torque to keep it spinning at constant

Voltage!

Connect loop to resistance R use I=V/R:

I = A B sin() / R

Generator

vv

•

x

A generator consists of a square coil of wire with 40 turns, each side is 0.2 meters long, and it is spinning with angular velocity = 2.5 radians/second in a uniform magnetic field B=0.15 T. Determine the direction of the induced current at instant shown. Calculate the maximum emf and torque if the resistive load is 4.

= NA B sin() Units?

= NI A B sin() Units?

Generator

vv

•

x

A generator consists of a square coil of wire with 40 turns, each side is 0.2 meters long, and it is spinning with angular velocity = 2.5 radians/second in a uniform magnetic field B=0.15 T. Determine the direction of the induced current at instant shown. Calculate the maximum emf and torque if the resistive load is 4.

= NA B sin()

= NI A B sin()

Note: Emf is maximum at =90

Note: Torque is maximum at =90

= (40) (0.2m)2 (0.15T) (2.5 radians/s)

= 0.6 Volts

= 40*I0.15A*(0.2m)2 * 0.15 T* 1

= 0.036 Newton-meters

maxmax

emfI

R

0.60.15

4

VA

Power Transmission,Preflight 16.5

A generator produces 1.2 Giga watts of power, which it transmits to a town 10 km away through copper power lines. How low does the line resistance need to be in order to consume less than 10% of the power transmitted from the generator at 120 Volts?

I = Current leaving/returning to the generator

Find I?

R = Line resistance for 12 Megawatt loss in lines

So why use high voltage lines?

Power Transmission,Preflight 16.5

A generator produces 1.2 Giga watts of power, which it transmits to a town 10 km away through copper power lines. How low does the line resistance need to be in order to consume less than 10% of the power transmitted from the generator at 120 Volts?

I = 107 P = I V so 1.2 109 = 120 I or I = 107 amps

R = 1.2 10-6 P = I2 R so 1.2 108 = (107)2 R or

R = 1.2 10-6

This would require a cable more than 40 feet in diameter!!

Large current is the problem. Since P=IV, use high voltage and low current to deliver power.

of Cu = 10-8 -m

1 inch square copper wire has about 0.1 ohm resistance in 7 km

Transformers

Increasing current in primary creates an increase in flux through primary and secondary.

iron

VsVp

tNV pp

tNV ss

Same t

p

s

p

s

N

N

V

V

Energy conservation! IpVp = IsVs

R

(primary) (secondary)

NSNP

Key to efficient power distribution

Preflight 13.6The good news is you are going on a trip to France. The bad news is that in France the outlets have 240 volts. You remember from Phy1152 that you need a transformer, so you wrap 100 turns around the primary. How many turns should you wrap around the secondary if you need 120 volts out to run your hair dryer?

iron

VsVp

R

1) 50 2) 100 3) 200

(primary) (secondary)

NSNP

Preflight 13.6The good news is you are going on a trip to France. The bad news is that in France the outlets have 240 volts. You remember from Phy1161 that you need a transformer, so you wrap 100 turns around the primary. How many turns should you wrap around the secondary if you need 120 volts out to run your hair dryer?

1 2

1 2

V V

N N

iron

VsVp

R

1 22

1

N VN

V

1) 50 2) 100 3) 200

100*12050

240

V

V (primary) (secondary)

NSNP

A 12 Volt battery is connected to a transformer that has a 100 turn primary coil, and 200 turn secondary coil. What is the voltage across the secondary after the battery has been connected for a long time?

1 2 3 4

25% 25%25%25%

1. Vs = 0

2. Vs = 6

3. Vs = 12

4. Vs = 24

A 12 Volt battery is connected to a transformer that has a 100 turn primary coil, and 200 turn secondary coil. What is the voltage across the secondary after the battery has been connected for a long time?

Transformers depend on a change in flux so they only work for alternating currents!

1 2 3 4

25% 25%25%25%

1. Vs = 0

2. Vs = 6

3. Vs = 12

4. Vs = 24

Transformers• Key to Modern electrical system• Starting with 120 volts AC– Produce arbitrarily small voltages.– Produce arbitrarily large voltages.

• Nearly 100% efficient

In a transformer the side with the most turns always has the larger peak voltage. (T/F)

1 2

0%0%

1. True2. False

In a transformer the side with the most turns always has the larger peak current. (T/F)

1 2

0%0%

1. True2. False

In a transformer the side with the most turns always dissipates the most power. (T/F)

1 2

0%0%

1. True2. False