Generators and Transformers

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Generators and Transformers
Physics 102 Lecture 11

• Todays lecture will cover Textbook Sections
  20.2, 20.6

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Exam I Results

• Average score 65
• Not as good as I had hoped for but still not bad

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Review Magnetic Flux

• B A cos(f)
• Units is T-m2

f is angle between normal and B
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Review Induction

• Faradays Law
• Magnitude of induced EMF given by
• 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

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Magnetic Flux Examples
Example
A conducting loop is inside a solenoid (BmonI).
What happens to the flux through the loop when
you
Increase area of solenoid?
Nothing
Increase area of loop?
Increases
Increase current in solenoid?
Increases
F ? B A cos(f)
Rotate loop slightly?
Decreases
48
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Magnetic Flux II
Example
A solenoid (BmonI) is inside a conducting loop.
What happens to the flux through the loop when
you
Increase area of solenoid
Increases
Increase area of loop
Nothing
Increase current in solenoid
Increases
F ? B A cos(f)
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7
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? / ?
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Generators and EMF
EMF is voltage!

• B A cos(?) B A cos(?t)
• eloop -??/?t
• w B A sin(?)
• w B A sin(wt)

eloop w B A sin(wt) ? BA cos(wt)
flux is maximum when emf is 0 And vice versa
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ACT Generators and EMF

• w A B sin(q)

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3
1
At which time does the loop have the greatest emf
(greatest ??/ ?t)?
1) Has greatest flux, but q 0 so e 0. 2)
Example weve studied, q ? 30 so e ? wAB/2. 3)
Flux is zero, but q 90 so e wAB.
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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!

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Preflights 11.1, 11.2, 11.3
q 30?
Flux is decreasing at moment shown. 46 got
correct.
When q30, the EMF around the loop
is increasing decreasing not changing
48 32 20
EMF is increasing!
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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
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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) (0.2)2 (0.15) (2.5) 0.6 Volts
v
q
x
t NI A B sin(q)
Note Emf is maximum at q90
N2 w A2 B2 sin2(q)/R (40)2 (2.5)
(0.2)4 (0.15)2/4 0.036 Newton-meters
Note Torque is maximum at q90
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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?

Example
P IV Power delivered by generator through
lines I P/V 1.2x109 W/120 V 10,000,000
Amps in lines!
P I2R Power lost in lines 10,000,0002
(.01) 1.0 Giga Watt Lost in Lines!
Large current is the problem. Since PIV, use
high voltage and low current to deliver power. If
V 12,000 Volts, loose 0.0001 Giga Watts!
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Transformers

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

!!!Volt!!
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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
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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
49 16 35

R
Vp
e
Vs
By halving the number of turns around the
secondary you decrease the voltage in the
secondary by half.
40
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ACT Transformers
iron
Transformers depend on a change in flux so they
only work for alternating currents!
Vp
Vs
R

• 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 3) Vs 12 4) Vs 24
45
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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.

True
False (has smaller current)
False (equal)
All of them will!
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See You Monday!
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