Transcript Generators and Transformers

Physics 102: Lecture 11
Generators and Transformers
• Today’s lecture will cover Textbook
Sections 20.2, 6
Physics 102: Lecture 11, Slide 1
Review: Two uses of RHR’s
• Force on moving charge in
Magnetic field
+ + + +v
F
I
– Thumb: v (or I)
– Fingers: B
– Palm: F on + charge
Palm: out of page.
• Magnetic field produced by
moving charges
– Thumb: I (or v for + charges)
– Fingers: where you want to know B
– Palm: B
Physics 102: Lecture 11, Slide 2
Thumb: out
Fingers: up
Palm: left.
x
•
Review: Two uses of RHR’s
• Force on moving
charge in Magnetic
field
• Magnetic field produced by
moving charges
– Thumb: I (or v for + charges)
– Fingers: curl along B field
Physics 102: Lecture 11, Slide 3
F
I
– Thumb: v (or I)
– Fingers: B
– Palm: F on + charge
+ + + +v
Palm: out of page.
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:
 
Physics 102: Lecture 11, Slide 4

  i
 f
t
t f  ti
Review: Rotation Variables
v, , f, T
• Velocity (v):

– How fast a point moves.
– Units: usually m/s
r
• Angular Frequency ():
– How fast something rotates.
– Units: radians / sec
v
v
v= r
• Frequency ( f ):
– How fast something rotates.
– Units: rotations / sec = Hz
f =  / 2
• Period (T):
– How much time one full rotation takes.
– Units: usually seconds
Physics 102: Lecture 11, Slide 5
T = 1 / f = 2
/
Generators and EMF
EMF is voltage!
side 1 = v B L sin(q)
v = r
side 1 = r B L sin(q)
side 2 = r B L sin(q)
loop = side 1 + side 2
 2r B L sin(q)
2rL = A
loop =  A B sin(q)
loop =  A B sin(t)
Physics 102: Lecture 11, Slide 6
1
•

v
2
AB
x
q
v
r

t
AB
ACT: Generators and EMF
 =  A B sin(q)
•
q
x
1
2
3
At which time does the loop have the greatest emf
(greatest / t)?
Physics 102: Lecture 11, Slide 7
ACT: Generators and EMF
 =  A B sin(q)
•
θ
x
1
2
3
At which time does the loop have the greatest emf
(greatest / t)?
1) Has greatest flux, but q = 0 so  = 0.
2) (Preflight example) q  30 so   AB/2.
3) Flux is zero, but q = 90 so  = AB.
Physics 102: Lecture 11, Slide 8
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
Physics 102: Lecture 11, Slide 9
– Just before: lines enter from top.
– Just after: lines enter from bottom.
– Big change!
Preflights
11.1, 11.2, 11.3
•

v
v
Flux is _________ at moment shown.
Increasing
x
q  30
r
decreasing
not changing
When q=30°, the EMF around the loop is:
increasing
decreasing
not changing
Physics 102: Lecture 11, Slide 10
q  30
EMF is increasing!

q
Preflights
11.1, 11.2, 11.3
•

Flux is decreasing at moment shown.
v
v
x
q  30
r
When q=30°, the EMF around the loop is:
q  30
increasing
decreasing
not changing
Physics 102: Lecture 11, Slide 11
EMF is increasing!

q
Generators and Torque
 =  A B sin(q)
Voltage!
Connect loop to resistance R use I=V/R:
I =  A B sin(q) / R
Recall:
t = A B I sin(q)
=  A2 B2 sin2(q)/R
•

v
x
r
Torque, due to current and B field, tries to slow
spinning loop down. Must supply external
torque to keep it spinning at constant 
Physics 102: Lecture 11, Slide 12
q
v
Generator
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 4W.
 = NA B  sin(q)
Units?

v
t = NI A B sin(q)
Physics 102: Lecture 11, Slide 13
Units?
x
•
v
Generator
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 4W.
 = NA B  sin(q)
= (40) (0.2)2 (0.15) (2.5)
= 0.6 Volts
t = NI A B sin(q)
= N2  A2 B2 sin2(q)/R
= (40)2 (2.5) (0.2)4 (0.15)2/4
= 0.036 Newton-meters
Physics 102: Lecture 11, Slide 14

•
v
v
x
q
Note: Emf is
maximum at q=90
Note: Torque is
maximum at q=90
Power Transmission,
Preflight 11.5
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?
Physics 102: Lecture 11, Slide 15
Power Transmission,
Preflight 11.5
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=
P = I2 R so 1.2  108 = (107)2 R or
R = 1.2  10-6 W
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.
Physics 102: Lecture 11, Slide 16
Transformers
Key to efficient power distribution
Increasing current in primary
creates an increase in flux
through primary and secondary.

Vp  N p
t

Vs   N s
t

iron
~
Vp
V
s
Same /t
Vs N s

Vp N p
Energy conservation!
Physics 102: Lecture 11, Slide 17
I p Vp = I s Vs
NP
NS
(primary)
(secondary)
R
Preflight 11.6
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 P102 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

~
Vp
V
s
Physics 102: Lecture 11, Slide 18
NP
NS
(primary)
(secondary)
R
Preflight 11.6
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 P102 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
Vs N s

Vp N p
3) 200

 Vs 
120 
N s  N p    100
  50
 240 
 Vp 
Physics 102: Lecture 11, Slide 19
~
Vp
V
s
NP
NS
(primary)
(secondary)
R
ACT: Transformers
iron
Vp
V
s
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
Physics 102: Lecture 11, Slide 20
3) Vs = 12
NP
NS
(primary)
(secondary)
4) Vs = 24
R
ACT: Transformers
Transformers depend on a
change in flux so they only
work for alternating
currents!
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
Physics 102: Lecture 11, Slide 21
3) Vs = 12
iron
Vp
V
s
NP
NS
(primary)
(secondary)
4) Vs = 24
R
Transformers
• Key to Modern electrical system
• Starting with 120 volts AC
– Produce arbitrarily small voltages.
– Produce arbitrarily large voltages.
• Nearly 100% efficient
!!!Volt!!
Physics 102: Lecture 11, Slide 22
Exam Prep Questions
•
In a transformer the side with the most turns always has the larger peak
voltage. (T/F)
•
In a transformer the side with the most turns always has the larger peak
current. (T/F)
•
In a transformer the side with the most turns always dissipates the most power.
(T/F)
•
Which of the following changes will increase the peak voltage delivered by a
generator
– Increase the speed it is spinning.
– Increase the area of the loop.
– Increase the strength of the magnetic field.
Physics 102: Lecture 11, Slide 23
See you next time!
• Read Sections 20.9, 21.1, 3-4
Physics 102: Lecture 11, Slide 24