Transcript Generators and Transformers

Physics 1161: Lecture 16
Generators
• Textbook Sections 23-6 – 23-10
http://www.walter-fendt.de/ph14e/electricmotor.htm
http://www.walter-fendt.de/ph14e/generator_e.htm
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
F
I
– Thumb: v (or I)
– Fingers: B
– Palm: F on + charge
+ + + +
Palm: out of page.
I
v
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:
 

t

f  i
tf  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
T=1/f=
2 / 
Generators and EMF
EMF is voltage!
side 1 = v B L sin(q)
1
•
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)

v
2 x
AB
q
v
r

t
AB
At which time does the loop have the
greatest emf (greatest / t)?
1. 1
2. 2
3. 3
43%
32%
25%
1
2
3
At which time does the loop have the
greatest emf (greatest / t)?
1. 1
2. 2
3. 3
60%
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.
26%
14%
1
2
3
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!
Preflights
16.1, 16.2, 16.3
•

v
v
Flux is _________ at moment shown.
Increasing
x
decreasing
q  30
r
not changing
q  30
EMF is increasing!
When q=30°, the EMF around the loop is:
increasing
decreasing
not changing

q
Preflights
16.1, 16.2, 16.3
•

v
v
Flux is decreasing at moment shown.
q  30
x
r
When q=30°, the EMF around the loop is:
increasing
q  30
EMF is increasing!
decreasing
not changing

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 
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
v
t = NI A B sin(q)
Units?
•
x
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) (0.2m)2 (0.15T) (2.5 radians/s)
v
v
= 0.6 Volts
q
x
t = NI A B sin(q)
I m ax 
em f m ax
R
•

0.6V
4W
 0.15 A
t = 40*I0.15A*(0.2m)2 * 0.15 T* 1
= 0.036 Newton-meters
Note: Emf is maximum at
q=90
Note: Torque is maximum at
q=90
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
R = 1.2  10-6 W
P = I V so 1.2  109 = 120 I or I = 107 amps
P = I2 R so 1.2  108 = (107)2 R or
R = 1.2  10-6 W
 of Cu = 10-8 W-m
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 P=IV, use high voltage and low current
to deliver power.
Transformers
Key to efficient power distribution
Increasing current in primary
creates an increase in flux
through primary and secondary.
Vp  N
iron

p
t


Vs   N s
~
Vp
Vs
t
Same /t
Vs
Vp

NP
Ns
N
(primary)
p
Energy conservation!
IpVp = IsVs
NS
(secondary)
R
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
iron
out to run your hair dryer?
1) 50
2) 100
3) 200

~
Vp
Vs
NP
(primary)
NS
(secondary)
R
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
iron
out to run your hair dryer?
1) 50
2) 100
V1

N1
N2 
N 1V 2
V1
3) 200

V2
~
Vp
Vs
N2

100 *120V
240V
 50
NP
(primary)
NS
(secondary)
R
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.
Vs = 0
Vs = 6
Vs = 12
Vs = 24
25%
1
25%
25%
2
3
25%
4
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.
Transformers depend on a change in flux
so they only work for alternating currents!
Vs = 0
Vs = 6
Vs = 12
Vs = 24
25%
1
25%
25%
2
3
25%
4
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. True
2. False
0%
1
0%
2
In a transformer the side with the
most turns always has the larger peak
current. (T/F)
1. True
2. False
0%
1
0%
2
In a transformer the side with the
most turns always dissipates the most
power. (T/F)
1. True
2. False
0%
1
0%
2