addendum – chapter 21
DESCRIPTION
Addendum – Chapter 21. Mutual inductance –. Circulation of currents in one coil can generate a field in the coil that will extend to a second, close by device. Flux Changes. Suppose i 1 CHANGES. Current (emf) is induced in 2 nd coil. Mutual Inductance. - PowerPoint PPT PresentationTRANSCRIPT
ADDENDUM – CHAPTER 21
Mutual inductance –
Circulation of currents in one coil can generate a field in the coil that will extend to a second, close by device.
Suppose i1 CHANGES
Flux Changes
Current (emf) isinduced in 2nd
coil.
Mutual Inductance
i1 creates a field that (partially) passes through the second coil.
As i1 changes, the flux through coil 2 changes and an emf (and current i2) are created.
The two coils are mutually linked by what we call an “inductance”
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i2
Watch Out!
Exam #2 one week from today. Chapters 20 & 21 Same format but possibly one set of multiple choice
questions that you hate. You should already be studying.
QUIZ on Friday – Chapter #21 Today we continue with the chapter. We should
finish it on Friday. Maybe. No study session on Monday next week We will have a study session on Tuesday morning
like last time. Details to follow.
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This schedule is now in effect:This schedule is now in effect:
PHY2054 Problem Solving/Office Hours ScheduleRoom MAP-318
Monday Tuesday Wednesday Thursday FridayBindell 8:30-9:15AM 8:30-9:15AM 8:30-9:15AM
Bindell 11:00-12:00PM10:30 - 11:15
AM* 10:30-11:30AMDubey 12:00-1:00PM 1:30-2:45PM
These sessions will be used both for office hours and problem solving. Students from anysection of 2054 are invited to stop by for assistance in course materials (problems, etc.)
Note: There will be times when the room may not be available. In that case we will use our individual offices.
* In Office Dr. Dubey's hours are for problem
solving only.
Mutual Inductance
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i2
12
2
~
#1. coil
incurrent the todue #2 coil
influx magnetic The
iB
B
t
iM
tNemf
iMN
ki
B
B
121
2122
12122
12
mutual Inductance
Note the form:
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i
NM something
Think of this when we define INDUCTANCEINDUCTANCE (L) ofa small coil in the next section.
UNIT: henry
The two coils
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Remember – the magneticfield outside of the solenoidis pretty much zero.
Two fluxes (fluxi?) are the same!Two fluxes (fluxi?) are the same!
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One solenoid is centered inside another. The outer one has a length of 50.0 cm and contains 6750 coils, while the coaxial inner solenoid is 3.0 cm long and 0.120 cm in diameter and contains 15 coils. The current in the outer solenoid is changing at 37.5 A/s. (a) What is the mutual inductance of these solenoids? (b) Find the emf induced in the inner solenoid
Length = 0.5 metersN=6750 coils
n=6750/.5=1.35E04 turn/meter
Magnetic field INSIDE the smaller coilis the same as in the larger coil andis given by:
iiniB 7.11035.1104 4701
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One solenoid is centered inside another. The outer one has a length of 50.0 cm and contains 6750 coils, while the coaxial inner solenoid is 3.0 cm long and 0.120 cm in diameter and contains 15 coils. The current in the outer solenoid is changing at 37.5 A/s. (a) What is the mutual inductance of these solenoids? (b) Find the emf induced in the inner solenoid
iniB 7.101
24
22
1013.1
)100/106.0(
mArea
cmmcmrAreacoilsmaller
mVVt
Nemf
VVt
i
t
iBA
B
B
B
11102.715
102.75.371092.11092.1
1092.1
3222
3442
42
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One solenoid is centered inside another. The outer one has a length of 50.0 cm and contains 6750 coils, while the coaxial inner solenoid is 3.0 cm long and 0.120 cm in diameter and contains 15 coils. The current in the outer solenoid is changing at 37.5 A/s. (a) What is the mutual inductance of these solenoids? (b) Find the emf induced in the inner solenoid
iniB 7.101
mH
ti
emfM 297.0
37
1011 32
Self-inductance –
Any circuit which carries a varying current self-induced from it’s own magnetic field is said to
have INDUCTANCE (L).
An inductor resists CHANGESCHANGES in the current going through it.
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An inductor resists CHANGESCHANGES in the current going through it.
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An inductor resists CHANGESCHANGES in the current going through it.
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Inductance Defined
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i
NL B
If the FLUX changes a bit during a short time t, then the current will change by a small amount i.
t
iL
tN
NLi
B
B
This is actually acalculus equation
Faraday says this is the emf!
So …
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t
iLemf
E=
The UNIT of “Inductance – L” of a coil is the henry.
SYMBOL:
There should bea (-) sign but weuse Lenz’s Lawinstead!
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Consider “AC” voltage
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V1
Maximum Change@t
Minimum Change@t
The transformer
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FLUX is the same throughboth coils (windings). 2
2
1
1
222
111
N
V
N
V
tNVemf
tNVemf
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Input/Output Impedance (Resistance)
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!resistance
inputan like looks
)/(
(Lossless)
2121
1
2211
1
2
1
2
NN
R
I
V
So
VIVI
PowerPower
N
N
V
V
outin
Remember that a Capacitor stored ENERGY? U=(1/2)CV2
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interval
iLiU
iLiUt
iLiP
t
iLV
ViPower
i
i
LiLI
i
Li
DU
IInduction
U=Area=(1/2)LI2
SO …
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Energy Stored in a capacitorThe energy stored in a capacitor with capacitance C and a voltage V is
U=(1/2)LI2
The Energy stored is in the Magnetic Field
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Consider a solenoid with N turns that is very long. We assume that the field is uniform throughout its length, ignoring any “end effects”. For a long enough solenoid, we can get away with it for the following argument. Maybe.
il
NniB 00
Energy Storage in Inductor
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0
0
22
2
1
2
1
2
1
BlNi
il
NB
NiBAU
BA
il
NLiU
l
NL
B
B
B
20
0
2
0
2
0
2
0
2
1ED
2
1
V
UDensity
2
1
2
1
2
1
ECapacitor
BEnergy
VBlABBA
BlU
Back to Circuits
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Induction
Series LR Circuit
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RL or LR Series Circuit
Switch is open .. no current flows for obvious reasons.
Switch closed for a long time: Steady current,
voltage across the inductor is zero. All voltage (E) is across the resistor.
i=E/R04/21/23Induction
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RL or LR Series Circuit
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i
t
E/R
When the switch opens, current change is high and back emf from L is maximum.
As the current increases, more voltage is across R, the rate of change of I decreasesand as the current increases, it increases more slowly.
RL Circuit
When L=0, the current rises very rapidly (almost instantly)
As L increases, it takes longer for the current to get to its maximum.
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RL Circuit - Kirchoff Stuff
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0
i
iLiRemf
constant) (time
)1(
)1(
/
)/(
R
L
eR
i
eR
i
Solution
t
tLR
E
E
The Graphic Result – Current Growth
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e= 2.71828…
63.01
1
e63% of
maximum}
Decay – Short out the battery
Magnetic field begins to collapse, sending its energy into driving the current.
The energy is dissipated in the resistor.
i begins at maximum (E/R) and decays.04/21/23Induction
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Solution
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)( /teR
i E
Up and Down and Up and Down and …..
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