Physics 7B - AB Lecture 2 April 10 Recap examples Steady-State Energy Density Model Applied to Fluid Circuit

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Physics 7B - ABLecture 2April 10Recap
examples Steady-State Energy Density
ModelApplied to Fluid Circuit Electrical
Circuit

• Lecture slides available athttp//physics.ucdavi
  s.edu/physics7

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Course Website http//physics.ucdavis.edu/physics7
Click on Physics 7B-A/B
Today Quiz 1!
Next week Lecturer 3 Dr. Kevin Klapstein
April 16 My office hr is cancelled.
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Current I VS Fluid velocity v
Remember Energy Density Equation ? a.k.a. Fluid
Transport Equation/Extended Bernoulli eq.
?P (1/2)??(v2) ? g?h IR Epump/V
Current I is Volumetric flow rate How much
water (in terms of volume) flows through a
section of a pipe per unit time. So it has the
unit of volume per second m3/s.
I vs v
Fluid velocity is how fast fluid is moving. So
it has the unit of distance per second.
velocity m/s
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Recap on Fluids
Basic rules for looking at fluids

• Energy (density) conservation
• a.k.a. Energy Density Model
• (P2 P1) (1/2)?(v22 v12) ? g( h2 h1)
  IR1?2 ?1?2

2. Current Conservation Current entering
current leaving
3. Pressures where two fluids systems touch are
equal
4. Resistance is proportional to length
5. ALWAYS, pick two points within the SAME fluid
system to apply 1 2!
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Current is shown flowing down the pipe shown.
Choose the correct statement.
1
2
(1) I1 I2 (2) I1 gt I2 (3) I1 lt I2 (4) Cannot
tell
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Current is shown flowing down the pipe shown.
Choose the correct statement.
1
2
(1) I1 I2 (2) I1 gt I2 (3) I1 lt I2 (4) Cannot
tell
7
Current is shown flowing down the (R0) pipe
shown. Fluid is flowing from 1 to 2.Choose the
correct statement
1
2
Pumping this way
(1) I1 I2 (2) I1 gt I2 (3) I1 lt I2 (4) Cannot
tell
8
Current is shown flowing down the (R0) pipe
shown. Fluid is flowing from 1 to 2.Choose the
correct statement
1
2
Pumping this way
(1) I1 I2 (2) I1 gt I2 (3) I1 lt I2 (4) Cannot
tell
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Current is shown flowing down the pipe shown.
Choose the correct statement.
1
2
(1) v1 v2 (2) v1 gt v2 (3) v1 lt v2 (4) Cannot
tell
10
Current is shown flowing down the pipe shown.
Choose the correct statement.
1
2
(1) v1 v2 (2) v1 gt v2 (3) v1 lt v2 (4) Cannot
tell
11
Current is shown flowing down the (R0) pipe
shown. Fluid is flowing from 1 to 2.Choose the
correct statement
1
2
Pumping this way
(1) v1 v2 (2) v1 gt v2 (3) v1 lt v2 (4) Cannot
tell
12
Current is shown flowing down the (R0) pipe
shown. Fluid is flowing from 1 to 2.Choose the
correct statement
1
2
Pumping this way
(1) v1 v2 (2) v1 gt v2 (3) v1 lt v2 (4) Cannot
tell
What energy system changed ?
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Pumping this way
The following shows a pipe without dissipation
(R0) with a pump attached. On which side is the
pressure greater?
1
2
(1) Side 1 (2) Side 2 (3) Not enough information
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Pumping this way
The following shows a pipe without dissipation
(R0) with a pump attached. On which side is the
pressure greater?
1
2
(1) Side 1 (2) Side 2 (3) Not enough information
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2
The following shows a resistanceless pipe (R0)
with a pump attached. On which side is the
pressure greater?
1
Pumping this way
(The change in height is 2 m from 1 to 2)
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2
The following shows a resistanceless pipe (R0)
with a pump attached. On which side is the
pressure greater?
1
Pumping this way
(The change in height is 2 m from 1 to 2)
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1
3
2
Assume no dissipation, i.e., R 0.
How does P1, P2 , P3 compare?
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1
3
2
Same height (approximately)1,3 have the same
speed (same area, current conserved) 2 is faster
(smaller area, current conserved)
No pumps between 1 and 3Assume no resistance
between 1 and 3.This implies P1 P3 gt P2.
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1
3
2
Small amount of resistance modifies this.
Pressures are P1 gt P3 gt P2
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1
3
2
Large amount of resistance modifies this.
Pressures are P1 gt P2 gt P3
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Recap and Examples on
Electrical circuits
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Analogies between Fluid and Electrical circuits
Fluids Electricity
Deals with Fluid flow Charge flow
Current Water flowing through a cross-section of pipe per unit time Electric charge flowing through a wire per unit time
v Indicator of kinetic energy (neglected)
h Indicator of gravitational potential energy (neglected)
R Relates current and thermal energy loss Relates current and thermal energy loss
Energy stored /unit volume or charge Pressure Voltage
(P2 P1) (1/2)?(v22 v12) ? g( h2 h1)
IR1?2 ?1?2
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Analogies between Fluid and Electrical circuits
Fluids Electricity
Deals with Fluid flow Charge flow
Current Water flowing through a cross-section of pipe per unit time Electric charge flowing through a wire per unit time
v Indicator of kinetic energy (neglected)
h Indicator of gravitational potential energy (neglected)
R Relates current and thermal energy loss Relates current and thermal energy loss
Energy stored /unit volume or charge Pressure Voltage
(V2 V1) (1/2)?(v22 v12) ? g( h2 h1)
IR1?2 ?1?2
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Analogies between Fluid and Electrical circuits
Fluids Electricity
Deals with Fluid flow Charge flow
Current Water flowing through a cross-section of pipe per unit time Electric charge flowing through a wire per unit time
v Indicator of kinetic energy (neglected)
h Indicator of gravitational potential energy (neglected)
R Relates current and thermal energy loss Relates current and thermal energy loss
Energy stored /unit volume or charge Pressure Voltage
(V2 V1) IR1?2 ?1?2 Or ?V ? IR
Energy Density Equation a.k.a. transport equation
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Energy Density Equation applied to Electrical
Circuitsa.k.a. transport equation, loop rule
(V2 V1) IR1?2 ?1?2 Or ?V ? IR
The change in the electrical potential energy per
charge, (what we call voltage, or voltage drop),
as we move from one point to another point will
increase due to energy added by a battery or
generator and will decrease due to the transfer
of electric potential energy per charge to
thermal energy system.
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Current (charge) conservationa.k.a. junction
rule (everything that flows into a junction must
be equal to everything that flows out)
A
B
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Electric PowerElecric energy is useful to us
because it can be easily transformed into other
forms of energy, e.g. hair dryer, lightbulb
Power rate at which energy is transformed by an
electric device Energy transformed/unit
time Ex. 120Watt 120 Joule/sec
1200 Watts
5000 - 8000 Watts
40 - 120Watts
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Electric PowerElecric energy is useful to us
because it can be easily transformed into other
forms of energy, e.g. hair dryer, lightbulb
120V
Power (?V) x I I2R
Rbulb
Rhair dryer
1200 Watts
Rclothes dryer
40 - 120Watts Bright ness of a bulb
5000 - 8000 Watts
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Bulbs 1 and 2 are connected with a battery as
shown to the right. The bulbs have different
Resistances. Which statement must be true?
R1
R2
2
1

1. The two bulbs have the same voltage different,
   ?V, across them and that ?V is half the battery
   voltage.
2. The two bulbs are equally bright.
3. The two bulbs and the battery have all the same
   current through them.
4. All of the above must be true.
5. None of the above must be true.

Note For electrical circuits, wires connecting
circuit elements are assumed to have zero
resistance.
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Bulbs 1 and 2 are connected with a battery as
shown to the right. The bulbs have different
Resistances. Which statement must be true?
R1
R2
2
1

1. The two bulbs have the same voltage different,
   ?V, across them and that ?V is half the battery
   voltage.
2. The two bulbs are equally bright.
3. The two bulbs and the battery have all the same
   current through them.
4. All of the above must be true.
5. None of the above must be true.

Note For electrical circuits, wires connecting
circuit elements are assumed to have zero
resistance.
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If the four bulbs in the figure are identical and
the batteries are identical, which circuit puts
out more light?
(Remember brightness depends on the power
transformed)
R
R
R

• 1 emits more light.
• The two emit the same
• amount of light.
• 2 emits more light.

R
?
?
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If the four bulbs in the figure are identical and
the batteries are identical, which circuit puts
out more light?
For a review of circuit analysis, refer to P.21
of the course text (Method of Equivalent
Reduction)
(Remember brightness depends on the power
transformed)
R
R
R
From todays lecture, For circuit1 R1equivalent
R/2, so I1 ?/R1equi. (2 ?)/R As bulbs are
identical, half of I1 flows through each
bulb. ?Power bulb in circuit 1 ((I1/2)2R
?/R2R ?2/R lt gives the measure of
brightness of a bulb in circuit 1 For circuit2
R2equivalent 2R, so I2 ?/R2equi. ?/(2R) and
this I2 flows through both bulbs. Power bulb in
circuit 2 I22R ( ?/2R)2R ?2/4R lt gives
the measure of brightness of a bulb in circuit 2
R
?
?
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If the four bulbs in the figure are identical and
the batteries are identical, which circuit puts
out more light?
(Remember brightness depends on the power
transformed)

• 1 emits more light.
• The two emit the same
• amount of light.
• 2 emits more light.

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If the two bulbs in the circuit 1 are NOT
identical, which bulb puts out more light?
(Remember brightness depends on the power
transformed)
RA

• Bulb A emits more light.
• The two emit the same
• amount of light.
• Bulb B emits more light.

RA gt RB
RB
Example Solve this for ? 6V, RA 3 Ohm, RB 1
Ohm
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If the two bulbs in the circuit 1 are NOT
identical, which bulb puts out more light?
(Remember brightness depends on the power
transformed)
RA

• Bulb A emits more light.
• The two emit the same
• amount of light.
• Bulb B emits more light.

RA gt RB
RB
Example Solve this for ? 6V, RA 3 Ohm, RB 1
Ohm You should find, IA 2A, IB 6A, and PA
12Watts, PB 36Watts
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Be sure to write your name, ID number DL
section!!!!!
1 MR 1030-1250 Dan Phillips
2 TR 210-430 Abby Shockley
3 TR 440-700 John Mahoney
4 TR 710-930 Ryan James
5 TF 800-1020 Ryan James
6 TF 1030-1250 John Mahoney
7 W 1030-1250 Brandon Bozek
7 F 210-430 Brandon Bozek
8 MW 800-1020 Brandon Bozek
9 MW 210-430 Chris Miller
10 MW 440-700 Marshall Van Zijll
11 MW 710-930 Marshall Van Zijll