Generators

1
Generators
Physics 1161 Lecture 16

• Textbook Sections 23-6 23-10
• http//www.walter-fendt.de/ph14e/electricmotor.htm
  
• http//www.walter-fendt.de/ph14e/generator_e.htm

2
Review Two uses of RHRs

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

B
I
F
Palm out of page.

• Magnetic field produced by moving charges
• Thumb I (or v for charges)
• Fingers curl along B field

I
3
Review Induction

• Lenzs 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 (VIR) additional
  B-field.
• Flux decreasing gt B-field in same direction as
  original
• Flux increasing gt B-field in opposite direction
  of original
• Faradays Law
• Magnitude of induced EMF given by

4
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

w
v
v
r
v ? r

• Frequency ( f )
• How fast something rotates.
• Units rotations / sec Hz
• Period (T)
• How much time one full rotation takes.
• Units usually seconds

f ? / 2?
T 1 / f 2? / ?
5
Generators and EMF
EMF is voltage!
eside 1 v B L sin(q)
eside 1 wr B L sin(q) eside 2 wr B L
sin(q) eloop eside 1 eside 2 2wr B
L sin(q)

• 2rL A

eloop w A B sin(q) eloop w A B sin(wt)
6
At which time does the loop have the greatest emf
(greatest ??/ ?t)?

1. 1
2. 2
3. 3

7
At which time does the loop have the greatest emf
(greatest ??/ ?t)?

1. 1
2. 2
3. 3

1) Has greatest flux, but q 0 so e 0. 2)
(Preflight example) q ? 30 so e ? wAB/2. 3) Flux
is zero, but q 90 so e wAB.
8
ComparisonFlux 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!

9
Preflights 16.1, 16.2, 16.3
q 30?
Flux is _________ at moment shown. Increasing de
creasing not changing
When q30, the EMF around the loop
is increasing decreasing not changing
EMF is increasing!
10
Preflights 16.1, 16.2, 16.3
q 30?
Flux is decreasing at moment shown.
When q30, the EMF around the loop
is increasing decreasing not changing
EMF is increasing!
11
Generators and Torque

• w A B sin(q)

Connect loop to resistance R use IV/R I w A
B sin(q) / R
w

q
v
v
r
Recall t A B I sin(q) w A2 B2
sin2(q)/R
x
Torque, due to current and B field, tries to
slow spinning loop down. Must supply external
torque to keep it spinning at constant w
12
Generator
Example
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 w 2.5
radians/second in a uniform magnetic field B0.15
T. Determine the direction of the induced current
at instant shown. Calculate the maximum emf and
torque if the resistive load is 4W.

• NA B w sin(q) Units?

w

v
v
t NI A B sin(q) Units?
x
13
Generator
Example
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 w 2.5
radians/second in a uniform magnetic field B0.15
T. Determine the direction of the induced current
at instant shown. Calculate the maximum emf and
torque if the resistive load is 4W.

• NA B w sin(q)

w

v
(40) (0.2m)2 (0.15T) (2.5 radians/s) 0.6 Volts
v
q
x
t NI A B sin(q)
Note Emf is maximum at q90

• t 40I0.15A(0.2m)2 0.15 T 1
• 0.036 Newton-meters

Note Torque is maximum at q90
14
Power Transmission,Preflight 16.5
Example

• 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?
15
Power Transmission,Preflight 16.5
Example

• 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
? of Cu 10-8 ?-m
R 1.2 ? 10-6 ? P I2 R so 1.2 ? 108
(107)2 R or
R 1.2 ? 10-6 ?
1 inch square copper wire has about 0.1 ohm
resistance in 7 km
This would require a cable more than 40 feet in
diameter!! Large current is the problem. Since
PIV, use high voltage and low current to deliver
power.
16
Transformers
Key to efficient power distribution

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

iron

R
Vp
e
Vs
Same DF/Dt
Energy conservation! IpVp IsVs
17
Preflight 13.6

• The 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
1) 50 2) 100 3) 200

R
Vp
e
Vs
18
Preflight 13.6

• The 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?

iron
1) 50 2) 100 3) 200

R
Vp
e
Vs
19
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. Vs 0
2. Vs 6
3. Vs 12
4. Vs 24

20
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. Vs 0
2. Vs 6
3. Vs 12
4. Vs 24

21
Transformers

• Key to Modern electrical system
• Starting with 120 volts AC
• Produce arbitrarily small voltages.
• Produce arbitrarily large voltages.
• Nearly 100 efficient

22
In a transformer the side with the most turns
always has the larger peak voltage. (T/F)

1. True
2. False

23
In a transformer the side with the most turns
always has the larger peak current. (T/F)

1. True
2. False

24
In a transformer the side with the most turns
always dissipates the most power. (T/F)

1. True
2. False