Physics 212 Lecture 17, Slide 1

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Physics 212 Lecture 17
2
Music

• Who is the Artist?
• Oscar Peterson
• Kenny Barron
• Dave Brubeck
• Thelonius Monk
• Marcus Roberts

CD
Piano Master ! Why? Hes
playing tomorrow at Krannert
Jazz and Barbeque !! Sold out since June,
though sigh
3
Last Time
time t dt e Bav0
A rectangular loop (sides a,b, resistance R,
mass m) coasts with a constant velocity v0 in
x direction as shown. At t 0, the loop enters a
region of constant magnetic field B directed in
the z direction. What is the velocity of the
loop when half of it is in the field?
x x x x x x x x x x x x x x x x x
x x x x x x x x x x x
a
x
4
Calculation
t dt e Bav0
y
A rectangular loop (sides a,b, resistance R,
mass m) coasts with a constant velocity v0 in
x direction as shown. At t 0, the loop enters a
region of constant magnetic field B directed in
the z direction. What is the velocity of the
loop when half of it is in the field?
B
x x x x x x x x x x x x x x x x x
x x x x x x x x x x x
b
v0
a
x
This is not obvious, but we know v must decrease
( all that was asked on the exam) !! Why?
Fright points to left Acceleration
negative Speed must decrease
5
Calculation
y
A rectangular loop (sides a,b, resistance R,
mass m) coasts with a constant velocity v0 in
x direction as shown. At t 0, the loop enters a
region of constant magnetic field B directed in
the z direction. What is the velocity of the
loop when half of it is in the field?
B
x x x x x x x x x x x x x x x x x
x x x x x x x x x x x
b
v0
a
x
e Bav0
Which of these plots best represents the
velocity as a function of time as the loop moves
form entering the field to halfway through ?
(A) (D)

• Why (D), not (A)?
• F is not constant, depends on v

Challenge Look at energy
6
Follow-Up
y
A rectangular loop (sides a,b, resistance R,
mass m) coasts with a constant velocity v0 in
x direction as shown. At t 0, the loop enters a
region of constant magnetic field B directed in
the z direction. Some time later it leaves the
region as shown What is the direction of the net
force on the loop in the position shown?
B
x x x x x x x x x x x x x x x x x
x x x x x x x x x x x
b
v
a
x
(A) y (B) -y (C) x
(D) -x (E) no net force
Flux is decreasing into the screen
Force on loop decreases speed as it must Energy
being dissipated in heating resistance
7
Prelecture 17
8
Things you identified as difficult
The stuff involving the calculations of the
inductor, in the prelecture. Please explain the
direction of the current during discharge. The
current stuff with the switches and infinity In
the prelecture there was talk of a voltage jump
on the inductor after switches were thrown
disconnecting it from a battery. This was
confusing.
9
From the prelecture
10
What this really means
Voltage induced across L tries to keep I constant

L
current I
Inductors hate it when the current changes
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Inside your i-clicker
12
I
L
R
13
How to think about RL circuits Episode 1 When no
current is flowing initially
I0
L
R
VBATT
14
How to think about RL circuits Episode 2 When
steady current is flowing initially
IV/R
L
R
15
VL
VBATT
t L/R
Lecture
Prelecture
No The resistance is simply twice as big in one
case.
16
Circuit in Preflight
L
R
IL0
V
R
Current through inductor cant change abruptly
17
4) In the circuit above, the switch has been open
for a long time, and the current is zero
everywhere. At time t0 the switch is closed.
What is the current I through the vertical
resistor immediately after the switch is closed?
( is in the direction of the arrow) A) I
V/R B) I V/2R C) I 0 D) I -V/2R E) I
-V/R
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Circuit in Preflight
L
R
IL
V
0 (current all going through the
short circuit inductor)
R
A long time later the current in the circuit is
no-longer changing.
VL 0
Inductor looks like a short circuit
19
5) In the circuit above, the switch has been open
for a long time, and the current is zero
everywhere. At time t0 the switch is closed.
What is the current I through the vertical
resistor after the switch has been closed for a
long time? ( is in the direction of the arrow)
A) I V/R B) I V/2R C) I 0 D) I -V/2R
E) I -V/R
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Circuit in Preflight
L
R
ILV/R
V
R
Current through inductor cant change abruptly.
I is the same just before and just after switch
opens V/R.
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7) After a long time, the switch is opened,
abruptly disconnecting the battery from the
circuit.
What is the current I through the vertical
resistor immediately after the switch is
opened? ( is in the direction of the arrow)
A) I V/R B) I V/2R C) I 0 D) I -V/2R
E) I -V/R
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1) Two solenoids are made with the same cross
sectional area and total number of turns.
Inductor B is twice as long as inductor A
Compare the inductance of the two solenoids
A) LA 4 LB B) LA 2 LB C) LA LB D) LA
(1/2) LB E) LA (1/4) LB
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2)  You are given 50 meters of wire and told you
must make the largest inductor you can, with the
constraint that its total volume must be 25 cm3.
Which geometry will give the greatest inductance?
(You may assume the inductance is given by the
formula derived for an infinite solenoid.) A) A
shorter solenoid with larger cross section B) A
longer solenoid with a smaller cross section
C) It doesn't matter, once the volume and length
of wire are specified, the inductance is
determined
D 50m N x 2pr
N D / 2pr
n N/z D / 2prz
24
Calculation
The switch in the circuit shown has been open for
a long time. At t 0, the switch is
closed. What is dIL/dt, the time rate of change
of the current through the inductor immediately
after switch is closed
R1
R2
V
L
R3
C

• Conceptual Analysis
• Once switch is closed, currents will flow through
  this 2-loop circuit.
• KVR and KCR can be used to determine currents as
  a function of time.

• Strategic Analysis
• Determine currents immediately after switch is
  closed.
• Determine voltage across inductor immediately
  after switch is closed.
• Determine dIL/dt immediately after switch is
  closed.

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Calculation
The switch in the circuit shown has been open for
a long time. At t 0, the switch is
closed. What is dIL/dt, the time rate of change
of the current through the inductor immediately
after switch is closed
R1
R2
V
L
R3
INDUCTORS Current cannot change discontinuously
!
26
Calculation
The switch in the circuit shown has been open for
a long time. At t 0, the switch is
closed. What is dIL/dt, the time rate of change
of the current through the inductor immediately
after switch is closed
R1
R2
V
L
R3
IL(t0) 0
We know IL 0 immediately after switch is closed
27
Calculation
The switch in the circuit shown has been open for
a long time. At t 0, the switch is
closed. What is dIL/dt, the time rate of change
of the current through the inductor immediately
after switch is closed
R1
R2
V
L
R3
I2(t0) V/(R1R2R3)
VL(t0) 0
The voltage across the inductor, VL, is also
equal to the voltage across R2 R3 The voltage
across R2 R3 I2(R2 R3) Therefore
28
Calculation
The switch in the circuit shown has been open for
a long time. At t 0, the switch is
closed. What is dIL/dt, the time rate of change
of the current through the inductor immediately
after switch is closed
R1
R2
V
L
R3
VL(t0) V(R2R3)/(R1R2R3)
The time rate of change of current through the
indu ctor (dIL /dt) VL /L
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Follow Up 1
The switch in the circuit shown has been closed
for a long time. What is I2, the current
through R2 ? (Positive values indicate current
flows to the right)
R1
R2
V
L
R3
After a long time, dI/dt 0 Therefore, the
voltage across L 0 Therefore the voltage across
R2 R3 0 Therefore the current through R2 R3
must be zero !!
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Follow Up 2
The switch in the circuit shown has been closed
for a long time. At t 0, the switch is
opened. What is I2, the current through R2
immediately after switch is opened ? (Positive
values indicate current flows to the right)
R1
R2
IL
V
L
R3
Current through inductor immediately AFTER switch
is opened IS THE SAME AS the current through
inductor immediately BEFORE switch is opened
Immediately BEFORE switch is opened IL V/R1
Immediately AFTER switch is opened IL flows in
right loop Therefore, IL -V/R1
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Strategy Question
A solenoid inductor with I 3A flowing through
its turns, has a volume 0f 1.5X10-3 m3. A
uniform B field inside the solenoid fills this
volume and has a magnitude of 0.08 T. Find the
total heat generated in the resistor R2 35W,
after the switch is opened and the current falls
to zero.
R1
B
V
R2

• Question Where do we start? What is our
  strategy?

• This is a little different. My plan had been to
  see if anyone could suggest a strategy.
• Since we didnt have time to get to this
  question, Ill suggest one.
• We are given the current, the volume, and the
  magnetic field.
• We can use the values for B and the volume to
  calculate the total energy stored in the
  inductor.
• We can then assume that all of this energy will
  eventually be dissipated as heat in the resistor.

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Strategy Question
A solenoid inductor with 3A flowing through its
turns, has a volume 0f 1.5X10-3 m3. A uniform B
field inside the solenoid fills this volume and
has a magnitude of 0.08 T. The total heat
generated in the resistor R 35W, is 3.82 J.
What is the inductance of the solenoid?
R1
B
V
R2

• Question Where do we start? What is our
  strategy?

• This is a little different. My plan had been to
  see if anyone could suggest a strategy.
• Since we didnt have time to get to this
  question, Ill suggest one.
• We can now use the current I to answer this
  question
• The total energy stored in an inductor is ½ LI2
• We calculated the total energy on the previous
  slide (would have been 3.82 J)
• Use the current and total energy to calculate L