physics 2112 unit 18 - college of dupage · 2020. 4. 1. · electricity & magnetism lecture 18,...
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Physics 2112
Unit 18
Today’s Concepts:A) Induction
B) RL Circuits
Electricity & Magnetism Lecture 18, Slide 1
Where we are…..
Unit 17, Slide 2
Just finished
introducing
magnetism
Will now apply
magnetism to AC
circuits
Remember Example 17.6 (solenoid)??
Unit 17, Slide 3
What if you only had the outer set of loops?
Would changing current in that induce anything?
1. Changing current in outer
set of loops
2. Caused changing magnetic
field in inner loops
3. Induced changing current in
inner loops.
Self Inductance
Electricity & Magnetism Lecture 18, Slide 4
IL B
dt
dIL
dt
LId
dt
d B −=−=
−=)(
Define:
Depends only on the
geometry of the coils
Voltage drop in a coil
…caused by changes in the
current in that same coil
L
What is the inductance of a long coil of wire (a solenoid)?
Example 18.1 (Inductance of Solenoid)
Electricity & Magnetism Lecture 18, Slide 5
Increasing current
What the minus sign means…..
Electricity & Magnetism Lecture 18, Slide 7
dt
dIL−=
DV < 0VA > VB
A B
Acts like a resistor
IAB DVAB
zrnLB
22
0 =
volumen *2
0=
decreasing current
What the minus sign means…..
Electricity & Magnetism Lecture 18, Slide 8
dt
dIL−=
DV > 0VA < VB
A B
Acts like a battery
IAB DVAB
However you try to change the current through an inductor, the inductor resists that change.
current I
L
dIdt
L = −L
emf induced across L tries to keep I constant.
Inductors prevent discontinuous current changes!
It’s like inertia!
What this really means:
Electricity & Magnetism Lecture 18, Slide 9
Units of inductance are Henrys (H) [Tm2/A]
RL
VBATT
I = 0
Time Constant
Electricity & Magnetism Lecture 18, Slide 10
R
L=
)1( /teR
VI −−=
R=120WL
12V= VBATT
S
Example 18.2 (Current in Solenoid)
Electricity & Magnetism Lecture 18, Slide 11
R
L=)1( /te
R
VI −−=
A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached to a 120W resistor and a 12V battery.
What is the current through the resistor 0.01sec after the switch is closed?
What is the current through the resistor 2.0 sec after the switch is closed?
Would the current have been at 0.01sec if the inductor had an internal resistance of 20W?
RL
At t = 0:I = 0
VL = VBATT
VR = 0
(L is like a giant resistor)
VBATT
I = 0
At t >> L/R:
VL = 0
VR = VBATT
I = VBATT/R
(L is like a short circuit)
R
I = V/R
L
VBATT
When no current is flowing initially:
How to think about RL circuits:
Electricity & Magnetism Lecture 18, Slide 12
VL
R
L=
I
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
In the circuit, the switch has been open for a long time, and the current is zero everywhere.
At time t = 0 the switch is closed.
I
I
CheckPoint 2A
Electricity & Magnetism Lecture 18, Slide 13
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/RI
I
Confusion about question….
Electricity & Magnetism Lecture 18, Slide 14
C) there is no current at t=0
I mean a little “dt” of time after t=0
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
After a long time, the switch is opened, abruptly disconnecting the battery from the circuit.
CheckPoint 2B
Electricity & Magnetism Lecture 18, Slide 15
RL
VBATT
I = V/R
At t >> L/R:
I = 0
VL = 0
VR = 0
R
I = 0
LR
I = VBATT/R
VR = IR
VL = VR
At t = 0:
When steady current is flowing initially:
How to Think about RL Circuits Episode 2:
VL
R
L=
R
L=
Electricity & Magnetism Lecture 18, Slide 16
R
I
V = IRdIdt
V = L L
+
−
−
+
Why is there Exponential Behavior?
VL
R
L=
R
L=
Electricity & Magnetism Lecture 18, Slide 17
0=+ IRdt
dIL
whereR
L=
/0
/
0)( tLtR eIeItI −− ==
Prelecture:
RL
I
Lecture:
VL
VBATT
Did we mess up?
No: The resistance is simply twice as big in one case.
R
L=
Electricity & Magnetism Lecture 18, Slide 18
Quick comment…
Inside your i-clicker
” 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?”
What are Inductors and Capacitors Good For?
Electricity & Magnetism Lecture 18, Slide 19
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 1B) Case 2C) The same
CheckPoint 3A
Electricity & Magnetism Lecture 18, Slide 20
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 1B) Case 2C) The same
R
L
21 =
R
L
32 =
CheckPoint 3A
Electricity & Magnetism Lecture 18, Slide 21
A) Case 1B) Case 2C) The same
CheckPoint 3B
Electricity & Magnetism Lecture 18, Slide 22
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 1B) Case 2C) The same
Before switch moved: R
VI =
After switch moved:
RR
VVL 21 =
RR
VVL 32 =
CheckPoint 3B
Electricity & Magnetism Lecture 18, Slide 23
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 1B) Case 2C) The same
CheckPoint 3C
Electricity & Magnetism Lecture 18, Slide 25
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 the inductor larger?
A) Case 1B) Case 2C) The same
Immediately after: 21 II =
After awhile
1/
1t
IeI−
=
2/
2t
IeI−
=
21 >
CheckPoint 3C
Electricity & Magnetism Lecture 18, Slide 26
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 the inductor larger?
Energy Stored
Unit 18, Slide 27
VIdt
energydPower ==
)(
2
2
1LIEstored =
2
2
1
C
QEstored =
For inductor Recall for capacitor
Energy stored in
the magnetic field
Energy stored in
the electric field
R=100WL
12V= VBATT
S
Example 18.3 (Energy in Solenoid)
Electricity & Magnetism Lecture 18, Slide 28
A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached to a 120W resistor and a 12V battery.
What is the energy stored in the inductor 0.01sec after the switch is closed?
What is the energy stored in the inductor 2.0 sec after the switch is closed?
2
2
1LIEstored =
A. 0A
B. 4A
C. 6A
D. 12A
E. -4A
120V
The switch has been in the open position for a long
time in the circuit drawn above. What is the total
current out of the battery, Itot, immediately after the
switch is closed? (The inductor is “ideal”.)
Question
A. 0A
B. 4A
C. 6A
D. 12A
E. -4A
120V
The switch has been in the open position for a long
time in the circuit drawn above. What is the current
across the resistor, I1, immediately after the switch
is closed? (The inductor is “ideal”.)
Question
A. 0A
B. 4A
C. 6A
D. 12A
E. -4A
120
V
The switch has been in the open position for a long
time in the circuit drawn above. What is the current
across the inductor, I2, immediately after the switch
is closed? (The inductor is “ideal”.)
Question
A. 0V
B. 80V
C. 90V
D. 120V
E. 240V
120
V
The switch has been in the open position for a long
time in the circuit drawn above. What is the voltage
drop across the inductor immediately after the
switch is closed? (The inductor is “ideal”.)
Question
A. 0A
B. 4A
C. 6A
D. 12A
E. -4A
120V
The switch has been in the closed position for a
long time in the circuit drawn above. What is the
current across the inductor, I2? (The inductor is
“ideal”.)
Question
A. 0V
B. 80V
C. 90V
D. 120V
E. 240V
120
V
The switch has been in the closed position for a
long time in the circuit drawn above. What is the
voltage difference across the inductor immediately
after the switch is opened? (The inductor is “ideal”.)
Question
A. 0A
B. 4A
C. 6A
D. 12A
E. -4A
120V
The switch has been in the closed position for a
long time in the circuit drawn above. What is the
current across the inductor, I2 immediately after the
switch is open? (The inductor is “ideal”.)
Question
A. 6A/sec
B. 80A/sec
C. 90A/sec
D. 120A/sec
E. 240A/sec
120
V
The switch has been in the closed position for a
long time in the circuit drawn above. What is the
rate change for the current through the inductor
immediately after the switch is opened? (The
inductor is “ideal”.)
Question
A. VA > VB
B. VA = VB
C. VA < VB
120
V
The switch has been in the open position for a long
time in the circuit drawn above. Which point has a
higher electrical potential immediately after the
switch is closed? (The inductor is “ideal”.)
Question
A
B
A. VA > VB
B. VA = VB
C. VA < VB
120
V
The switch has been in the closed position for a
long time in the circuit drawn above. Which point
has a higher electrical potential? (The inductor is
“ideal”.)
Question
A
B
A. VA > VB
B. VA = VB
C. VA < VB
120
V
The switch has been in the closed position for a
long time in the circuit drawn above. Which point
has a higher electrical potential immediately after
the switch is opened? (The inductor is “ideal”.)
Question
A
B