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Unformatted text preview: Physics 212
Lecture 18 50
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0 Confused Avg = 2.7 Confident Physics 212 Lecture 18, Slide 1 Music
Who is the Artist?
A)
B)
C)
D)
E) Stephane Grappelli
Dave Brubeck
Itzhak Perlman & Oscar Peterson
Hot Club of Cowtown
Hot
Cowtown
Regina Carter Theme of the week
Jazz by violin players from other genres…
Pretty cool !!
Physics 212 Lecture 18, Slide 2 Physics 212
Lecture 18 50
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0 Confused Avg = 2.7 Confident Physics 212 Lecture 18, Slide 3 From the prelecture: Self Inductance Wrap a wire into a coil to make an “inductor”…
Wrap ε = L dI
dt Physics 212 Lecture 18, Slide 4 What this really means:
emf induced across L tries to keep I constant
induced
tries εL = L dI
dt L
current I
Inductors prevent discontinuous current changes !
It’s like inertia!
Physics 212 Lecture 18, Slide 5 Preflight 2
Two solenoids are made with the same cross sectional area and
Two
total number of turns. Inductor B is twice as long as inductor A
twice L = µ0 n 2π r 2 z
(1/2)2 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 50
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0 Physics 212 Lecture 18, Slide 6 WHAT ARE INDUCTORS AND CAPACITORS GOOD FOR? Inside your iclicker Physics 212 Lecture 18, Slide 7 How to think about RL circuits Episode 1:
How
Episode
When no current is flowing initially:
VL I=0
L τ = L/R I=V/R
R L R
I VBATT At t = 0:
I=0
VL = VBATT
VR = 0
(L is like a giant resistor) τ = L/R VBATT At t >> L/R:
At
VL = 0
VR = VBATT
I = VBATT/R (L is like a short circuit)
Physics 212 Lecture 18, Slide 8 Preflight 4
In the circuit above, the switch
In
has been open for a long time,
and the current is zero
everywhere. BB I At time t=0 the switch is closed.
At
What is the current I through the
What
vertical resistor immediately after
the switch is closed?
the
(+ is in the direction of the arrow)
A) I = V/R
A)
B) I = V/2R
C) I = 0
D) I = V/2R
D)
E) I = V/R I IL=0 40 Before: IL = 0 30 After: IL = 0 20
10 I = + V/2R
0 Physics 212 Lecture 18, Slide 9 RL Circuit (Long Time)
What is the current I through the vertical resistor after the
What
switch has been closed for a long time?
switch BB (+ is in the direction of the arrow)
(+
A) I = V/R
A)
B) I = V/2R
C) I = 0
D) I = V/2R
D)
E) I = V/R + + After a long time in any static circuit: VL = 0   KVR:
VL + IR = 0
Physics 212 Lecture 18, Slide 10
10 VBATT How to think about RL circuits Episode 2:
How
Episode
When steady current is flowing initially:
VL τ = L/R I=0
R L R L R I=V/R At t = 0:
I = VBATT/R
VR = IR
IR
VL = VR τ = L/R At t >> L/R:
At
I=0
VL = 0
VR = 0
Physics 212 Lecture 18, Slide 11
11 Preflight 6
After a long time, the switch is
After
opened, abruptly disconnecting
the battery from the circuit.
the
What is the current I through the
What
vertical resistor immediately after
the switch is opened?
the
(+ is in the direction of the arrow)
(+
A) I = V/R
A)
B) I = V/2R
C) I = 0
D) I = V/2R
D)
E) I = V/R
Current through inductor
Current
cannot change
DISCONTINUOUSLY
DISCONTINUOUSLY circuit when
circuit
switch opened
switch BB
50 L 40 IL=V/R R 30
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0 Physics 212 Lecture 18, Slide 12
12 Why is there exponential behavior ? V=L dI
dt L
+ + I − VL R τ = L/R V = IR
−
τ = L/R dI
L + IR = 0
dt
I (t ) = I 0e −tR / L = I 0e −t / τ L
where τ =
R
Physics 212 Lecture 18, Slide 13
13 I
L VL R VBATT τ = L/R Lecture: Prelecture: Did we mess up??
No: The resistance is simply twice as big in one case.
Physics 212 Lecture 18, Slide 14
14 Preflight 8
After long time at 0, moved to 1 After long time at 0, moved to 2
BB After switch moved, which case
After
has larger time constant?
has
A) Case 1
B) Case 2
C) The same L
τ1 =
2R L
τ2 =
3R 60
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0 Physics 212 Lecture 18, Slide 15
15 Preflight 10
After long time at 0, moved to 1 After long time at 0, moved to 2
BB Immediately after switch moved,
Immediately
in which case is the voltage
across the inductor larger?
across
A) Case 1
After switch moved:
B) Case 2
V
VL1 = 2 R
C) The same
R V
Before switch moved: I =
R VL 2 = V
3R
R 60
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0 Physics 212 Lecture 18, Slide 16
16 Preflight 12
After long time at 0, moved to 1 After long time at 0, moved to 2
BB After switch moved for finite time,
After
in which case is the current
through the inductor larger?
through
A) Case 1
After awhile
B) Case 2
I1 = Ie−t / τ
C) The same
1 Immediately after: I1 = I 2 I 2 = Ie −t / τ τ1 > τ 2 2 50
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0 Physics 212 Lecture 18, Slide 17
17 Calculation The switch in the circuit shown has
been open for a long time. At t = 0,
the switch is closed. R1
V What is dIL/dt, the time rate of
change of the current through the
inductor immediately after switch is
closed 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 212 Lecture 18, Slide 18
18 Calculation The switch in the circuit shown has
been open for a long time. At t = 0,
the switch is closed. R1
V R2
BB L IL = 0 R3 What is IL, the current in the inductor, immediately after the switch
is closed?
(A) IL =V/R1 up (B) IL =V/R1 down
(B) (C) IL = 0
(C) INDUCTORS: Current cannot change discontinuously !
INDUCTORS: Current Current through inductor immediately AFTER switch is closed
Current
AFTER switch
IS THE SAME AS
IS
the current through inductor immediately BEFORE switch is closed
the
BEFORE switch
Immediately before switch is closed: IL = 0 since no battery in loop
Immediately
since
Physics 212 Lecture 18, Slide 19
19 Calculation The switch in the circuit shown has
been open for a long time. At t = 0,
the switch is closed. R1
V R2
BB 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
R2 + R3
R1 + R2 + R3
R1
R2 + R3
We know IL = 0 immediately after switch is closed
R1
I
Immediately after switch is closed, V
Immediately
circuit looks like:
circuit I= R2 V
R1 + R2 + R3 R3 Physics 212 Lecture 18, Slide 20
20 Calculation The switch in the circuit shown has
been open for a long time. At t = 0,
the switch is closed. R1
V R2 I2
BB L R3 I2(t=0+) = V/(R1+R2+R3) IL(t=0+) = 0 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 RR R +R 23
2
3
(D) VL = V
(E) VL = V
R1 ( R2 + R3 )
R1 + R2 + R3 Kirchhoff’s Voltage Law, VLI2 R2 I2 R3 =0
VL = I2 (R2+R3)
VL = V
( R2 + R3 )
R1 + R2 + R3 Physics 212 Lecture 18, Slide 21
21 Calculation The switch in the circuit shown has
been open for a long time. At t = 0,
the switch is closed. R1 R2
BB V
What is dIL/dt, the time rate of
change of the current through the
inductor immediately after switch is
closed dI
V R2 + R3
dI
(A) L =
(B) L = 0
dt
L R1
dt 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 22
22 Follow Up 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) (A) I 2 = + V
R2 + R3 (B) I 2 = +
(B) V ( R2 R3 )
R1 + R2 + R3 R1 R2
BB V L (C) I 2 = 0 R3 (D) I 2 = − V
R2 + R3 After a long time, dI/dt = 0
After
dI/dt
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 23
23 Follow Up 2 The switch in the circuit shown has
been closed for a long time at which
point, the switch is opened. R1
V What is I2, the current through R2
immediately after switch is opened ?
(Positive values indicate current flows
to the right) (A) I2 = + V
R1 + R2 + R3 V (B) I 2 = + R 1 (C) I 2 = 0 R2 I2 IL BB L R3 V (D) I 2 = −
R (E) I 2 = − 1 V
R1 + R2 + R3 Current through inductor immediately AFTER switch is opened
Current
AFTER switch
IS THE SAME AS
IS
the current through inductor immediately BEFORE switch is opened
the
BEFORE switch
Immediately BEFORE switch is opened: IL = V/R1
BEFORE switch
Immediately AFTER switch is opened: IL flows in right loop
switch
Therefore, IL = V/R1
Physics 212 Lecture 18, Slide 24
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 Fall '10
 Selig
 Physics

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