Transcript Physics 102: Lecture 11

Physics 102: Lecture 11
Generators and Transformers
Physics 102: Lecture 11, Slide 1
Review: Magnetic Flux
B
f
= B A cos(f)
Units is T m2 = Wb
f is angle between normal and B
Physics 102: Lecture 11, Slide 2
Review: Induction
• Faraday’s Law
– Magnitude of induced EMF given by:
• Lenz’s Law
 

  i
 f
t
t f  ti
– 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
Physics 102: Lecture 11, Slide 3
Physics 102: Lecture 11, Slide 4
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!
 = B A cos(q) =B A cos(t)

loop = -/t
=  B A sin(q)
  B A sin(t)
loop =  B A sin(t)
 = BA cos(t)
flux is maximum when emf is 0
And vice versa
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
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
•

Flux is ___________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 10

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 11
q
v
Physics 102: Lecture 11, Slide 12
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)
=
=
t = NI A B sin(q)
=
=
=
Physics 102: Lecture 11, Slide 13

•
v
v
x
q
Power Transmission,
Preflight 11.5
A generator produces 1.2 Giga watts of power, which it transmits to a town 7
miles away through power lines with a total resistance 0.01 ohms. How
much power is lost in the lines if the energy is transmitted at 120 Volts?
P = Power delivered by generator through lines
Find I?
P = I2R Power lost in lines
Find Plost?
Large current is the problem. Since P=IV, use high
voltage and low current to deliver power.
If V = 12,000 Volts, loose 0.0001 Giga Watts!
Physics 102: Lecture 11, Slide 14
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

Physics 102: Lecture 11, Slide 18
~
Vp
Vs
NP
NS
(primary)
(secondary)
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 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 19
3) Vs = 12
iron
Vp
Vs
NP
NS
(primary)
(secondary)
4) Vs = 24
R
Physics 102: Lecture 11, Slide 20
Questions to Think About
•
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 21
Physics 102: Lecture 11, Slide 22