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Unformatted text preview: Physics 212
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Lecture 18 Physics 212 Lecture 18, Slide 1 Music
Who is the Artist?
A)
B)
C)
D)
E) Arturo Sandoval
Tiempo Libre
Chucho Valdes & AfroCuban Messengers
AfroFreddie Omar con su banda
Los Hombres Calientes
Hombres Calientes Theme of the week: Great Piano Players from Classic to
Current
He also did a spectacular show at Krannert last fall
Legendary Cuban piano player
Hasn’t been in the U.S. in seven years
A real treat !! Your
Your Comments
“OMG NO MORE MAGNETIC FIELDS. IM SOOOOOO
HAPPY
HAPPY”
“How can a neutral spiral of metal oppose the slowing
down of charge flow. I still don't have a warm and
fuzzy
fuzzy grasp of Faraday's law!!!!” Inductor stores energy in its
magnetic field! “I don't really get why the voltage doubles when
the switch is opened. I'd like some clarifications.
Thanks!
Thanks!”
“Checkpoint 2, what happens when the switch turns
on right away to the current” Difficult checkpoints today! “Can we go over the entire last checkpoint”
“How do you find the voltage across the inductor
when there is no power source?”
“Hooray for circuits”
“I HATE CIRCUITS....right when things started to become exciting with magnetism, we
have to go back to circuits...I'm really disliking the physics department at this moment”
“I'm going to need some inDUCTance tape to keep all this info from falling out of my brain.”
05 Physics 212 Lecture 18, Slide 3 Some
Some Exam Stuff
• Exam Next Wednesday ( Oct. 26) at 7:00
– Covers material in Lectures 9 – 18 (through today’s lecture)
– Bring your ID: Rooms determined by discussion section (see link)
– Conflict exam at 5:15 – sign up in your gradebook before TONIGHT
(Oct. 20, 10:00 p.m.)
– If you have conflicts with both of these, contact Prof. Park Physics 212 Lecture 18, Slide 4 News
News Flash
• Final exams:
– Wed. Dec 14 7:00 – 10:00 p.m.
– Thu. Dec. 15 1:30 – 4:30 p.m.
Dec 15
4:30 Physics 212 Lecture 18, Slide 5 From
From the prelecture: Self Inductance Wrap a wire into a coil to make an “inductor”… = L dI
dt Physics 212 Lecture 18, Slide 6 What
What this really means:
emf induced across L tries to keep I constant L = L dI
dt L
current I
Inductors prevent discontinuous current changes !
It’s like inertia!
Physics 212 Lecture 18, Slide 7 Checkpoint 1
Two
Two solenoids are made with the same cross sectional area and
total
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 “z increases by two but n decreases by 2. so .5^2*2=.5 for
Lb
Lb”
“number of turns and length cancel out”
“same amount of turns, only difference is z, which is 2” Physics 212 Lecture 18, Slide 8 Checkpoint 1
Two
Two solenoids are made with the same cross sectional area and
total
total number of turns. Inductor B is twice as long as inductor A LB 0 n 2r 2 z
(1/2)2 2 LB 1 L A
2 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
Physics 212 Lecture 18, Slide 9 WHAT ARE INDUCTORS AND CAPACITORS GOOD FOR? ” Can you have capacitors and inductors in the same circuit?
“why inductors are important as opposed to capacitors. why use one
instead of the other?” Inside your iclicker
i Physics 212 Lecture 18, Slide 10 How
How to think about RL circuits Episode 1:
Episode
When no current is flowing initially:
VL I=0
L I=V/R
I=V/R
R L = L/R R
I VBATT At t = 0:
I=0
VL = VBATT
VR = 0
(L is like a giant resistor) VBATT = L/R At t >> L/R:
VL = 0
VR = VBATT
I = VBATT/R (L is like a short circuit)
Physics 212 Lecture 18, Slide 11 Checkpoint 2a
In the circuit, the switch has
In
been open for a long time, and
the current is zero everywhere.
At
At time t=0 the switch is closed. What is the current I through the
vertical resistor immediately after
the
the switch is closed?
(+
(+ is in the direction of the arrow)
A)
A) I = V/R
B) I = V/2R
C) I = 0
D) I = V/2R
E) I = V/R “At t=0 the inductor will have a voltage drop of V so the
parallel resistor must have the same voltage drop and V=IR.”
“Since there is no current in the inductor, the current
through
through the vertical resistor will just be V/Req or V/2R”
“No current will go through the resistor at the start
because it will all go through the inductor.”
Physics 212 Lecture 18, Slide 12 Checkpoint 2a
In the circuit, the switch has
In
been open for a long time, and
the current is zero everywhere.
I At time t=0 the switch is closed. What is the current I through the
vertical resistor immediately after
the
the switch is closed? I IL=0 (+
(+ 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 Before:
Before: IL = 0
After: IL = 0
I = + V/2R
Physics 212 Lecture 18, Slide 13 RL Circuit (Long Time)
Wh
What is the current I through the vertical resistor after the
switch
switch has been closed for a long time?
time?
(+
(+ is in the direction of the arrow)
A)
A) I = V/R
B) I = V/2R
C) I = 0
D) I = V/2R
E) I = V/R
V/
V/ + + After a long time in any static circuit: VL = 0   KVR:
VL + IR = 0
Physics 212 Lecture 18, Slide 14 VBATT How
How to think about RL circuits Episode 2:
Episode
When steady current is flowing initially:
VL I=0
R L R L R I=V/R At t = 0:
I = VBATT/R
VR = IR
VL = VR = L/R = L/R At t >> L/R:
I=0
VL = 0
VR = 0
Physics 212 Lecture 18, Slide 15 Checkpoint 2b
After a long time, the switch is
After
the
opened,
opened, abruptly disconnecting
the battery from the circuit.
What is the current I through the
vertical
vertical resistor immediately after
the switch is opened?
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 “The voltage is the voltage of the battery, so the current
equals that voltage divided by the resistance. ”
“Immediately after the switch is opened, the current will
still be the same as right before the switch was opened
(after having been closed for a long time, so V/2R.”
“Doesn't change. No current when switch is opened.”
Physics 212 Lecture 18, Slide 16 Checkpoint 2b
After a long time, the switch is
After
the
opened,
opened, abruptly disconnecting
the battery from the circuit.
What is the current I through the
vertical
vertical resistor immediately after
the switch is opened?
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 circuit when
switch opened L
IL=V/R R Current through inductor
cannot change
DISCONTINUOUSLY
Physics
Physics 212 Lecture 18, Slide 17 Why is there exponential behavior ?
I V=L dI
dt L
+ VL + R = L/R V = IR = L/R dI
L IR 0
dt
I (t ) I 0e tR / L I 0e t / L
where R
Physics 212 Lecture 18, Slide 18 I
L VL R VBATT = L/R Lecture: Prelecture: Did we mess up??
No: The resistance is simply twice as big in one case.
Physics 212 Lecture 18, Slide 19 Checkpoint 3a
After long time at 0, moved to 1 After switch moved, which case
has larger time constant?
A) Case 1
B) Case 2
C) The same After long time at 0, moved to 2 “The time constant depends on L/R, and since R
total
total is smaller in case 1, the time constant is
greater. ”
“The resistance is greater in case 2 and the
constant is directly proportional to R.”
“Each closed loop has the same equivelant
resistance.” Physics 212 Lecture 18, Slide 20 Checkpoint 3a
After long time at 0, moved to 1 After long time at 0, moved to 2 After switch moved, which case
has larger time constant?
A) Case 1
B) Case 2
C) The same L
1 2R L
2 3R Physics 212 Lecture 18, Slide 21 Checkpoint 3b
After long time at 0, moved to 1 After long time at 0, moved to 2 Immediately after switch moved,
in which case is the voltage
across the inductor larger?
A) Case 1
B) Case 2
C) The same “The resistance in case 1 is smaller, so the current
is bigger ”
“resistors added in series in case two will
contribute to the greater voltage”
“The max voltage is twice the voltage of the
battery, which is the same in both cases”
Physics 212 Lecture 18, Slide 22 Checkpoint 3b
After long time at 0, moved to 1 After long time at 0, moved to 2 Immediately after switch moved,
in which case is the voltage
across
across the inductor larger?
A) Case 1
After switch moved:
B) Case 2
V
VL1 2 R
C) The same
Before switch moved: I V
R VL 2 R
V 3R
R Physics 212 Lecture 18, Slide 23 Checkpoint 3c
After long time at 0, moved to 1 After long time at 0, moved to 2 After switch moved for finite time, “Case one has a bigger time constant ”
in which case is the current
through the inductor larger? “Case 2 has a smaller time constant so the decay of
A) Case 1
current will be smaller, lasting longer. ”
B) Case 2
C) The same
“The current depends on the characteristics of
th
the inductor, therefore the current running
through will be same. ” Physics
Physics 212 Lecture 18, Slide 24 Checkpoint 3c
After long time at 0, moved to 1 After long time at 0, moved to 2 After switch moved for finite time,
in which case is the current
through
through the inductor larger?
A) Case 1
After awhile
B) Case 2
I1 Ie t / C) The same
1 Immediately after: I1 I 2 I 2 Ie t / 1 2 2 Physics 212 Lecture 18, Slide 26 Calculation
Calculation The switch in the circuit shown has
been
been open for a long time. At t = 0,
At
the switch is closed. What is dIL/dt, the time rate of
change of the current through the
th
inductor immediately after switch is
closed R1
V R2
L R3 • Conceptual Analysis
–
– Once switch is closed, currents will flow through this 2loop 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. Physics
Physics 212 Lecture 18, Slide 27 Calculation
Calculation The switch in the circuit shown has
been
been open for a long time. At t = 0,
At
the switch is closed. R1
V R2
L IL = 0 R3 Wh
What is IL, the current in the inductor, immediately after the switch
th
th
is closed?
(A) IL =V/R1 up (B) IL =V/R1 down (C) I L = 0 INDUCTORS: Current cannot change discontinuously !
Current through inductor immediately AFTER switch is closed
IS THE SAME AS
the current through inductor immediately BEFORE switch is closed
BEFORE
Immediately
Immediately before switch is closed: IL = 0 since no battery in loop
Physics
Physics 212 Lecture 18, Slide 28 Calculation
Calculation The switch in the circuit shown has
been
been open for a long time. At t = 0,
At
the switch is closed. R1
V R2
L R3 IL(t=0+) = 0 What is the magnitude of I2, the current in R2, immediately after the
switch is closed?
V
V
V
(A ) I 2 (B) I 2 ( C) I 2 (D) I 2 VR2 R3
(D)
R2 R3
R1 R2 R3
R1
R2 R3
We know IL = 0 immediately after switch is closed
R1
Immediately after switch is closed, V
circuit looks like: I I R2 V
R1 R2 R3 R3 Physics 212 Lecture 18, Slide 29 Calculation
Calculation The switch in the circuit shown has
been
been open for a long time. At t = 0,
At
the switch is closed. R1
V R2
L IL(t=0+) = 0 I2
R3 I2(t=0+) = V/(R1+R2+R3) Wh
What is the magnitude of VL, the voltage across the inductor,
immediately after the switch is closed?
(A) VL V R2 R3
R1 (B) VL V (C) VL 0 (D) VL V R2 R3
R2 R3
(E) VL V
R1 ( R2 R3 )
R1 R2 R3 Kirchhoff’s Voltage Law, VLI2 R2 I2 R3 =0
=0
VL = I2 (R2+R3)
VL V R2 R3 R1 R2 R3 Physics 212 Lecture 18, Slide 30 Calculation
Calculation The switch in the circuit shown has
been
been open for a long time. At t = 0,
At
the switch is closed. What is dIL/dt, the time rate of
change of the current through the
th
inductor immediately after switch is
closed dI
V R2 R3
dI
(A) L (B) L 0
dt
L R1
dt R1 R2 V L R3 VL(t=0+) = V(R2+R3)/(R1+R2+R3) dI
V R2 R3
(C) L dt
L R1 R2 R3 dI L V (D)
dt
L The time rate of change of current through the inductor (dIL /dt) = VL /L dI L V R2 R3 dt L R1 R2 R3
Physics 212 Lecture 18, Slide 31 Follow
Follow Up The switch in the circuit shown has
been
been closed for a long time. What is I2, the current through R2 ?
(Positive values indicate current flows
to the right) (A) I 2 V
R2 R3 (B) I 2 V ( R2 R3 )
R1 R2 R3 R1
V R2
L (C) I 2 0 R3 (D) I 2 V
R2 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 !! Physics 212 Lecture 18, Slide 32 Follow
Follow Up 2 The switch in the circuit shown has
been
been closed for a long time at which
point, the switch is opened. What is I2, the current through R2
immediately after switch is opened ?
(Positive values indicate current flows
to the right) (A) I 2 V
R1 R2 R3 (B) I 2 V
R1 R1
V (C) I 2 0 R2 I2 IL
L (D) I 2 R3 V
R1 (E) I 2 V
R1 R2 R3 Current through inductor immediately AFTER switch is opened
IS THE SAME AS
the current through inductor immediately BEFORE switch is opened
Immediately
Immediately BEFORE switch is opened: IL = V/R1
Immediately AFTER switch is opened: IL flows in right loop
Therefore, IL = V/R1
Physics 212 Lecture 18, Slide 33 ...
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 Fall '08
 Kim
 Physics

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