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11C.T. PanC.T. Pan 11
CAPACITANCE, CAPACITANCE, INDUCTANCE, INDUCTANCE, AND AND MUTUAL
INDUCTANCE MUTUAL INDUCTANCE
22C.T. PanC.T. Pan
6.1 The Capacitor6.1 The Capacitor
6.2 The Inductor6.2 The Inductor
6.3 Series6.3 Series--Parallel Combinations of Capacitance
Parallel Combinations of Capacitance and Inductanceand
Inductance
6.4 Mutual Inductance6.4 Mutual Inductance
22
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In this chapter, two new and important passive In this chapter,
two new and important passive linear components are
introduced.linear components are introduced.
They are ideal models.They are ideal models.
Resistors dissipate energy but capacitors and Resistors
dissipate energy but capacitors and inductors are energy storage
components.inductors are energy storage components.
33C.T. PanC.T. Pan 33
6.1 The Capacitor6.1 The Capacitor
44C.T. PanC.T. Pan 44
6.1 The Capacitor6.1 The CapacitorCircuit symbol and component
model.Circuit symbol and component model.
, ( ) t
C Cq C v q(t)= i d
q : chargeC : capacitance , in F(Farad)
τ τ⋅ ∫@
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55C.T. PanC.T. Pan 55
6.1 The Capacitor6.1 The Capacitor0
0
00
1 1 1( ) ( ) ( ) ( )
1( ) ( ) ( ) .......... (A)
( ) ..................... (B)
1 farad = 1 Coulomb/Volt
t t
C C C Ct
t
C C Ct
CC
v t i d i d i dC C C
v t v t i dC
dvdqi t Cdt dt
τ τ τ τ τ τ
τ τ
−∞= = +
+
= =
∫ ∫ ∫
∫@
The unit of capacitance is chosen to be farad in honor of The
unit of capacitance is chosen to be farad in honor of the English
physicist , Michael Faraday(1791the English physicist , Michael
Faraday(1791--1867). 1867).
66C.T. PanC.T. Pan 66
6.1 The Capacitor6.1 The CapacitorExample 1 : A parallelExample
1 : A parallel--plate capacitorplate capacitor
ε
C=
: the permittivity of the dielectric material between the
plates
Ad
ε
ε
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77C.T. PanC.T. Pan 77
6.1 The Capacitor6.1 The Capacitor
ε( )
( )2
2
( ) ( ) ( )
1( ) 02 2
c c c c
c c
cC C C
t
c
If v > 0 and i > 0 , or v < 0 and i < 0 the
capacitor is being charged.If v i < 0 , the capacitor is
discharging.
dv tp(t)= v t i t v t C
dtEnergy in a capacitor
qw p d C v tC
τ τ−∞
⋅
=
= = = ≥∫
Example 1 : (cont.)Example 1 : (cont.)
88C.T. PanC.T. Pan 88
6.1 The Capacitor6.1 The Capacitor
0
( ) ( )
1( ) ( ) ( )
lim ( ) ( ) , (0 ) (0 )
C
t
C C Ct
C C C C
C
b v t is a continuous function if there is only finite strength
energy sources inside the circuit.
v t v t i dC
v t v t v v
i.e. v (t
ε
ε
ε τ τ
ε
+
+ −
→
+ = +
+ = =
∫Q
C) can not change abruptly for finite i (t)
( ) . ,
C ca When v is constant , then i = 0.ie equivalent to open
circuit
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99C.T. PanC.T. Pan 99
6.1 The Capacitor6.1 The Capacitor
(c) An ideal capacitor does not dissipate energy . It
storesenergy in the electrical field .
(d) A nonideal capacitor has a leakage resistance
ESR : equivalent series resistance
1010C.T. PanC.T. Pan 1010
6.2 The Inductor6.2 The Inductor
iL0
λ
( ) ( ) , tt
L LL i v d
λ : flux linkage , in web - turnsL : inductance , in H
(Henry)
λ λ τ τ⋅ = ∫@
Circuit symbol and component model.Circuit symbol and component
model.
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1111C.T. PanC.T. Pan
( ) ( ) ( )
( ) ( ) ( )
( ) ( )
( ) ( ) ( )
( ) ( ) ( )
0
0
00
2
1 1 1
1 ( )
( )
Energy in an inductor 1 0 2
t t t
L L L Lt
t
L L Lt
LL
LL L L
t
L
i v d v d v dL L L
i t i t v d ALdi tdv t L B
dt dtdi t
p t v i Li tdt
w t p d Li t
τ τ τ τ τ τ
τ τ
λ
τ τ
−∞ −∞= = +
= + − − − − − − − − − −
= = − − − − − − − − − − − − −
= =
= = ≥
∫ ∫ ∫
∫
∫
6.2 The Inductor6.2 The Inductor
1212C.T. PanC.T. Pan
il
NA
H : magnetic field intensityH : magnetic field intensityB : flux
density B : flux density
,
, perm eability of the core
H d l N i
N iH l N i Hl
N iB Hl
µµ µ
=
= =
= =
∫ruuv
—
Example 2 : An InductorExample 2 : An Inductor6.2 The
Inductor6.2 The Inductor
: f lu xB d Aφ ∫ur ur
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1313C.T. PanC.T. Pan
il
NA
Example 2 : (cont.)Example 2 : (cont.)6.2 The Inductor6.2 The
Inductor
2
2
, f lu x l i n k a g e
A N iB AlA N iN
lA NL
i l
µφ
µλ φ
λ µ
= =
= =
∴ = =
1414C.T. PanC.T. Pan
6.2 The Inductor6.2 The InductorThe unit of inductance is the
henry (H) , named in honor The unit of inductance is the henry (H)
, named in honor of the American inventor Joseph Henry (1797of the
American inventor Joseph Henry (1797--1878) .1878) .
1H = 1 volt1H = 1 volt--second / amperesecond / ampere(a) when
(a) when iiL L is constant , then is constant , then vvLL=0 .=0
.
i.e.i.e. , equivalent to short circuit, equivalent to short
circuit(b) (b) iiLL(t) is a continuous function if there is only
finite (t) is a continuous function if there is only finite
strength source inside the circuit .strength source inside the
circuit .
( ) ( ) ( )
( ) ( ) ( ) ( )( ) ( )
0
1
lim , 0 0
. . can not change abruptly for finite .
t
L L Lt
L L L L
L L
i t i t v dtL
i t i t or i i
i e i t v t
τ+∈
+ −
∈→
+ ∈ = +
+ ∈ = =
∫
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1515C.T. PanC.T. Pan
6.2 The Inductor6.2 The Inductor(c) An ideal inductor does not
dissipate energy .(c) An ideal inductor does not dissipate energy
.
It stores energy in the magnetic field .It stores energy in the
magnetic field .
(d) A nonideal inductor contains winding resistance and (d) A
nonideal inductor contains winding resistance and parasitic
capacitance .parasitic capacitance .
1616C.T. PanC.T. Pan
6.2 The Inductor6.2 The InductorExample 3 : Under dc and steady
state conditions, Example 3 : Under dc and steady state
conditions,
find (a) I , Vfind (a) I , VCC & I& ILL , (b) W, (b) WCC
and Wand WLL
2
2
12 21 5
5 101 1 10 5021 2 2 42
L
C L
C
L
I I A
V I V
W J
W J
= = =+
= =
= × × =
= × × =
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1717C.T. PanC.T. Pan
6.2 The Inductor6.2 The Inductor(a)(a) The capacity of C and L
to store energy makes themThe capacity of C and L to store energy
makes them
useful as temporary voltage or current sources , i.e. , useful
as temporary voltage or current sources , i.e. , they can be used
for generating a large amount ofthey can be used for generating a
large amount ofvoltage or current for a short period of
time.voltage or current for a short period of time.
(b)(b) The continuity property of VThe continuity property of
VCC(t) and i(t) and iLL(t) makes (t) makes inductors useful for
spark or arc suppression andinductors useful for spark or arc
suppression andfor converting pulsating voltage into relativelyfor
converting pulsating voltage into relativelysmooth dc
voltage.smooth dc voltage.
1818C.T. PanC.T. Pan
6.2 The Inductor6.2 The Inductor
(c)(c) The frequency sensitive property of L and C makesThe
frequency sensitive property of L and C makesthem useful for
frequency discrimination.them useful for frequency
discrimination.
(eg. LP , HP , (eg. LP , HP , BP filters)BP filters)
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1919C.T. PanC.T. Pan
6.3 Series6.3 Series--Parallel Combinations ofParallel
Combinations ofCapacitance and InductanceCapacitance and
Inductance
N capacitors in parallelN capacitors in parallel
ii1 i2 iN
v c1 c2 cNL1 2
1 2
1
1 2
(0) (0)
N
N
N
k eqk
eq N
k
i i i idv dv dvc c cdt dt dt
dv dvc Cdt dt
C c c cv v
=
= + + +
= + + +
= =
∴ = + + +
=
∑
Q L
L
L1 2
1 2
(0) (0) (0)= =
N
N
v v vv v v v
= = == =
LL
2020C.T. PanC.T. Pan
6.3 Series6.3 Series--Parallel Combinations ofParallel
Combinations ofCapacitance and InductanceCapacitance and
Inductance
N capacitors in seriesN capacitors in series
LL
( ) ( ) ( )
( )
( ) ( )
( ) ( ) ( ) ( )
0
0
0
0
1 1
0
1 2
0 1 0 2 0 0
1
1 ( )
1
1 1 1 1
t
k kk t
tN N
k ok kk t
t
eq t
eq N
N
v t i d v tc
v i d v tc
i d v tC
C C C C
v t v t v t v t
τ τ
τ τ
τ τ
= =
= +
∴ = +
= +
∴ = + + +
= + + +
∫
∑ ∑∫
∫
Q
L
L
1 2 Ni i i= = =L
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2121C.T. PanC.T. Pan
6.3 Series6.3 Series--Parallel Combinations ofParallel
Combinations ofCapacitance and InductanceCapacitance and
Inductance
N inductors in seriesN inductors in series
L1 2
1 2
1
1 2
1 2
(0) (0) (0) (0)
N
N
N
k eqk
eq N
N
v v v vdi di diL L Ldt dt dt
di diL Ldt dt
L L L Li i i i
=
= + + +
= + + +
= =
∴ = + + +
= = =
∑
Q L
L
LL
1 2
1 2
(0) (0) (0)( ) (t)= = ( ) ( )
N
N
i i ii t i i t i t
= = == =
LL
2222C.T. PanC.T. Pan
6.3 Series6.3 Series--Parallel Combinations ofParallel
Combinations ofCapacitance and InductanceCapacitance and
Inductance
N inductors in parallelN inductors in parallel
L
( ) ( ) ( )
( )
( )
( ) ( ) ( ) ( )
0 0 0
0
0
1 0 2 0 01 2
01 1
0
1 2
0 1 0 2 0 0
1 1 1
1
1
1 1 1 1
t t t
Nt t tN
N Nt
ktk kk
t
teq
eq N
N
i i t vd i t vd i t vdL L L
vd i tL
vd i tL
L L L L
i t i t i t i t
τ τ τ
τ
τ
= =
= + + + + + +
= +
= +
∴ = + + +
= + + +
∫ ∫ ∫
∑ ∑∫
∫
L
L
L
1 2
1 2
N
N
v v v vi i i i
= = = =∴ = + + +Q L
L
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6.3 Series6.3 Series--Parallel Combinations ofParallel
Combinations ofCapacitance and InductanceCapacitance and
Inductance
Resistor Capacitor Inductor
V-I
I-V
P or W
series
parallel
dc case open circuit1 2eqC C C= +
1 2
1 2eq
C CCC C
=+
21 2
W Cv=
dvi Cdt
=
00
1( ) t
tv v t i dt
C= + ∫ V RI=
1 I VR
=
22VP I R
R= =
1 2eqR R R= +
1 2
1 2eq
R RRR R
=+
same
21 2
W Li=
1 2eqL L L= +
1 2
1 2eq
L LLL L
=+
short circuit
00
1( ) v t
ti i t d
Lτ= + ∫
div Ldt
=
In summaryIn summary
6.4 Mutual Inductance6.4 Mutual Inductance
2424C.T. PanC.T. Pan
Circuit symbol and model of coupling inductorsCircuit symbol and
model of coupling inductors
1i 2i
1v+
−2v
+
−1L 2L
12M LL11 , L, L22 : self inductances: self inductancesM : mutual
inductanceM : mutual inductanceunit : in H unit : in H
2
1 211
1 22
di div L Mdt dtdi div M Ldt dt
= +
= +
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6.4 Mutual Inductance6.4 Mutual Inductance
2525C.T. PanC.T. Pan
Example 4 : Example 4 : Mutual inductanceMutual inductance
1 2
1 1
Apply I , with i =0
H dl=N I⋅⋅∫ur v
2626C.T. PanC.T. Pan
Assume uniform magnetic field intensity HAssume uniform magnetic
field intensity H1 1 1 1
1 1
21 1 1 2 1
1 1 2 2
21 1 2 1 2
1 2 11 1
,
;
,
N I N IH B Hl l
A N IB d Al
A N I A N N IN Nl l
A N A N NL MI l I l
µµ
µφ
µ µλ φ λ φ
λ µ λ µ
= ∴ = =
= ⋅ =
= = = =
= =
∫
@ @
6.4 Mutual Inductance6.4 Mutual Inductance
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6.4 Mutual Inductance6.4 Mutual Inductance
2727C.T. PanC.T. Pan
Dot convention for mutually coupled inductors: Dot convention
for mutually coupled inductors: When the reference direction for a
current enters the When the reference direction for a current
enters the dotted terminal of a coil , the polarity of the induced
dotted terminal of a coil , the polarity of the induced voltage in
the other coil is positive at its correspondingvoltage in the other
coil is positive at its correspondingdotted terminal.dotted
terminal.
6.4 Mutual Inductance6.4 Mutual Inductance
2828C.T. PanC.T. Pan
ii11↗↗ , , vv11>0 , >0 , φ↗φ↗ , ( i, ( i22=0 )=0 )
Another dot of coil 2 should be placed in terminal c.Another dot
of coil 2 should be placed in terminal c.
V1>0 V2
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6.4 Mutual Inductance6.4 Mutual Inductance
2929C.T. PanC.T. Pan
Conceptually , one can connect a resistor at cd terminals. Then
i2 will be negative.The generated flux of i2 will oppose the
increasing of φdue to increasing i1 ( Lentz law ).Hence , another
dot should be placed at c terminal.
V1>0 V2
6.4 Mutual Inductance6.4 Mutual Inductance
3030C.T. PanC.T. Pan
In case , the other dot is placed at d terminal , then i2will be
positive.Hence , the generated flux of i2 will be added to the
increasing φ due to i1.
V1>0 V2
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6.4 Mutual Inductance6.4 Mutual Inductance
3131C.T. PanC.T. Pan
Then the induced voltage at coil two will increase Then the
induced voltage at coil two will increase and so will iand so will
i22..This will violate the conservation of energy. This will
violate the conservation of energy.
V1>0 V2
6.4 Mutual Inductance6.4 Mutual Inductance
3232C.T. PanC.T. Pan
The procedure for determining dot markingsThe procedure for
determining dot markings
Step1Step1 Assign current direction references for the
coils.Assign current direction references for the coils.
Step2Step2 Arbitrarily select one terminal of one coil and
Arbitrarily select one terminal of one coil and mark it with a
dot.mark it with a dot.
Step3Step3 Use the rightUse the right--hand rule to determine
the direction hand rule to determine the direction of the magnetic
flux due to the current of the otheof the magnetic flux due to the
current of the other r coil.coil.
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6.4 Mutual Inductance6.4 Mutual Inductance
3333C.T. PanC.T. Pan
Step4Step4 If this flux direction has the same direction as that
If this flux direction has the same direction as that of the first
dot terminal current , then the secondof the first dot terminal
current , then the seconddot is placed at the terminal where the
second dot is placed at the terminal where the second current
enters. Otherwise, the second dot should current enters. Otherwise,
the second dot should be placed at the terminal where the second
currentbe placed at the terminal where the second
currentleaves.leaves.
3434C.T. PanC.T. Pan 3434
6.4 Mutual Inductance6.4 Mutual InductanceExample 5 :
Determining dot markingsExample 5 : Determining dot markings
Step 1Step 1 : Assign : Assign ii11 , , ii22 , , ii33
directions.directions.
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3535C.T. PanC.T. Pan 3535
6.4 Mutual Inductance6.4 Mutual InductanceExample 5 :
(cont.)Example 5 : (cont.)
Step 2Step 2 : :
For coils 1 and 2, choose For coils 1 and 2, choose first dot as
followsfirst dot as follows
3636C.T. PanC.T. Pan 3636
6.4 Mutual Inductance6.4 Mutual InductanceExample 5 :
(cont.)Example 5 : (cont.)
For coils 1 and 3For coils 1 and 3
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3737C.T. PanC.T. Pan 3737
6.4 Mutual Inductance6.4 Mutual InductanceExample 5 :
(cont.)Example 5 : (cont.)
For coils 2 and 3For coils 2 and 3
3838C.T. PanC.T. Pan 3838
6.4 Mutual Inductance6.4 Mutual InductanceExample 5 :
(cont.)Example 5 : (cont.)Step 3Step 3 : :
Check the relative flux directions and determine the Check the
relative flux directions and determine the dot position at the
other coildot position at the other coil
For coil 1 and 2For coil 1 and 2and are in the same directionand
are in the same direction
1L 2L
12M
1φ 2φ
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3939C.T. PanC.T. Pan 3939
6.4 Mutual Inductance6.4 Mutual InductanceExample 5 :
(cont.)Example 5 : (cont.)
For coil 1 and 3For coil 1 and 3
and are in opposite directionand are in opposite direction
1L 3L
1φ 3φ
4040C.T. PanC.T. Pan 4040
6.4 Mutual Inductance6.4 Mutual InductanceExample 5 :
(cont.)Example 5 : (cont.)
For coil 2 and 3For coil 2 and 3
and are in opposite directionand are in opposite direction2φ
3φ
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4141C.T. PanC.T. Pan 4141
6.4 Mutual Inductance6.4 Mutual InductanceExample 5 :
(cont.)Example 5 : (cont.)
In summaryIn summary+
_
+
_
i1 i2
v1 v2L1 L2
M12
i3+
_v3L3
M13M23
31 21 1 12 13
31 22 12 2 23
31 23 13 23 3
didi div L M Mdt dt dt
didi div M L Mdt dt dt
didi div M M Ldt dt dt
= + −
= + −
= − − +
4242C.T. PanC.T. Pan 4242
6.4 Mutual Inductance6.4 Mutual Inductance
If the physical arrangement of the coils are not known, If the
physical arrangement of the coils are not known, the relative
polarities of the magnetically coupled coils the relative
polarities of the magnetically coupled coils can be determined
experimentally. We needcan be determined experimentally. We
need
a dc voltage source a dc voltage source VVSSa resistor a
resistor RR : to limit the current: to limit the currenta switch a
switch SSa dc voltmetera dc voltmeter
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4343C.T. PanC.T. Pan 4343
6.4 Mutual Inductance6.4 Mutual Inductance
Step 1Step 1 : Assign current directions and arbitrarily assign
: Assign current directions and arbitrarily assign one dot at coil
one.one dot at coil one.
1L 2L
4444C.T. PanC.T. Pan 4444
6.4 Mutual Inductance6.4 Mutual Inductance
Step 2Step 2 : Connect the setup as follows.: Connect the setup
as follows.
1L 2L
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4545C.T. PanC.T. Pan 4545
6.4 Mutual Inductance6.4 Mutual InductanceStep 3Step 3 :
Determine the voltmeter deflection when the : Determine the
voltmeter deflection when the
switch is closed.switch is closed.If the momentary deflection is
upscale, If the momentary deflection is upscale, thenthen
1L 2L
If the momentary deflection is downscale, If the momentary
deflection is downscale, thenthen
1L 2L
4646C.T. PanC.T. Pan 4646
The reciprocal property of the mutual inductance can beThe
reciprocal property of the mutual inductance can beproved by
considering the energy relationship .proved by considering the
energy relationship .Step 1Step 1 : i: i22=0 , i=0 , i11 increased
from zero to I .increased from zero to I .
1
11 1
12 21
1 1 1 2 2
11 1
1 10
211 1 1 10
( )
2
t
I
div Ldt
div Mdt
input power p v i v idiL idt
input energy w p d
LL i di I
τ
=
=
= +
=
=
= =
∫
∫
1i 2i
1v+
−2v
+
−1L 2L
12M
6.4 Mutual Inductance6.4 Mutual Inductance
-
Step2 Step2 : keep i: keep i11=I , i=I , i22 is increased from
zero to Iis increased from zero to I222 2
1 1 12 12
2 22 21 2 2
di didIv L M Mdt dt dt
di didIv M L Ldt dt dt
= + =
= + =
C.T. PanC.T. Pan 4747
2 1 1 2 2
2 212 1 2 2 ( )
p v I v idi diM I L idt dt
= +
= +
2 2
2 2
12 1 2 2 2 20 0
212 1 2 2 2
1 2
I I
w p d
M I di L i di
M I I L I
τ=
= +
= +
∫∫ ∫
Input powerInput power
6.4 Mutual Inductance6.4 Mutual Inductance
Input energyInput energy
2 21 2 1 1 2 2 1 2 12
1 12 2
w w w L I L I I I M= + = + +
C.T. PanC.T. Pan 4848
Total energy when iTotal energy when i11=I=I11 , i,
i22=I=I22
Similarly , if we reverse the procedure , by first Similarly ,
if we reverse the procedure , by first increasing iincreasing i2 2
from zero to Ifrom zero to I22 and then increasing iand then
increasing i11 from from zero to Izero to I11, the total energy is,
the total energy is
2 21 2 1 1 2 2 1 2 21
1 12 2
w w w L I L I I I M= + = + +
Hence , MHence , M1212=M=M2121=M=M
6.4 Mutual Inductance6.4 Mutual Inductance
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C.T. PanC.T. Pan 4949
1 2
0 110 , 2
1 1 , 2
1 ,
MkL L
k
k loosely coupling
k closely coupling
k unity coupling
≤ ≤
< <
≤ <
=
@
6.4 Mutual Inductance6.4 Mutual Inductance
Definition of coefficient of coupling kDefinition of coefficient
of coupling k
2 21 1 2 2 1 2
1 1 02 2
w L i L i Mi i= + ± ≥
2 21 1 2 2 1 2
1 1 02 2
L i L i Mi i+ − =
C.T. PanC.T. Pan 5050
According to dot convention chosen , the total energy According
to dot convention chosen , the total energy stored in the coupled
inductors should be stored in the coupled inductors should be
In particular , consider the limiting caseIn particular ,
consider the limiting case
21 21 2 1 2 1 2( ) ( ) 02 2
L Li i i i L L M− + − =
6.4 Mutual Inductance6.4 Mutual Inductance
The above equation can be put into the following form The above
equation can be put into the following form
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C.T. PanC.T. Pan 5151
Thus , Thus , ww(t) (t) ≧≧0 only if0 only if
1 2L L M≥
when iwhen i11 and iand i22 are either both positive or both
negative are either both positive or both negative Hence , kHence ,
k≦≦11
6.4 Mutual Inductance6.4 Mutual Inductance
C.T. PanC.T. Pan 5252
5Ω 20Ω
gigi
16Hi
2i 60Ω
1i
4Hi
Example 6 : Finding meshExample 6 : Finding mesh--current
equations for a circuit current equations for a circuit with
magnetically coupled coils.with magnetically coupled coils.
Three meshes and one Three meshes and one current source , only
need current source , only need two unknowns , say itwo unknowns ,
say i11 and and ii22
6.4 Mutual Inductance6.4 Mutual Inductance
Note : current iNote : current i4H 4H = i= i11(t)(t)current
icurrent i16H 16H = i= ig g -- ii22
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C.T. PanC.T. Pan 5353
Due to existence of mutual inductance M=8H , thereDue to
existence of mutual inductance M=8H , thereare two voltage terms
for each coil . are two voltage terms for each coil .
6.4 Mutual Inductance6.4 Mutual Inductance
One can use dependence source to eliminate the One can use
dependence source to eliminate the coupling relation as
follows.coupling relation as follows.
5Ω 20Ω
gigi 2
i 60Ω
1i
168 Hd idt
18 didt
C.T. PanC.T. Pan 5454
6.4 Mutual Inductance6.4 Mutual Inductance
1
12 1 2 1
2
2 1 2 2 1
,
4 8 ( ) 20( ) 5( ) 0
20( ) 60 16 ( ) 8 0
g g
g
Hence for i meshdi d i i i i i idt dt
For i meshd di i i i i idt dt
+ − + − + − =
− + + − − =
4H
5Ω 20Ω
gigi
16H2i
60Ω
1i+-
+-
168 Hd idt
18 didt
-
n Objective 1 : Know and be able to use the componentmodel of an
inductor
n Objective 2 : Know and be able to use the componentmodel of a
capacitor.
n Objective 3 : Be able to find the equivalent inductor
(capacitor) together with it equivalent initial condition for
inductors (capacitors) connected in series and in parallel.
C.T. PanC.T. Pan 5555
SummarySummary
C.T. PanC.T. Pan 5656
SummarySummary
Chapter Problems : 6.46.196.216.266.406.41
Due within one week.
nObjective 4 : Understand the component model of coupling
inductors and the dot convention as well as be able to write the
mesh equations for a circuit containing coupling inductors.