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Chapter #32 Inductance
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32.1: Self-Induction and Inductance
32.2: RL Circuits (15)
32.3: Energy in a Magnetic Field (8)
32.4: Mutual Inductance (8)
32.5: Oscillations in an LC Circuit (10)
32.6: The RLC Circuit
Self-Inductance
•  Self inductance:
changing current in
a coil induces a
current in itself.
d ( N ΦB )
d ΦB
=−
dt
dt
N ΦB = L i
E =− N
E =−
L=
d ( L i)
di
=− L
dt
dt
N ΦB
i
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Mutual Inductance
d ( N 2 Φ B2 )
d Φ B2
=−
dt
dt
N 2 Φ B2 = M 21 i1
•  Mutual
inductance:
changing
current in one
coil induces a
current in
another coil.
E2 =− N 2
d ( M 21 i1 )
di
E2 =−
=− M 21 1
dt
dt
M 21 =
N 2 ΦB 2
= M12
i1
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Units of Mutual Inductance and
Self Inductance
M 21 = M12 =
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N 2 ΦB 2
=M
i1
L=
1 [H] = 1 [Weber]/1 [A]
1 [H] = 1 [V⋅s]/1 [A]
1 [H] = 1 [Ω⋅s]
1 [H] = 1 [J]/1€[A2]
N ΦB
i
E =− L
di
dt
Experiment # 1
•
I = const,

B = const
•  No induced
emf
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Experiment # 2
•  Current increases:
the increasing flux
creates an induced
emf in the
direction opposite
to the battery.
•  No current change
- no emf
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Experiment # 3
•  Current decreases:
the decreasing flux
creates an induced
emf in the same
direction as the
battery.
•  No current change no emf
Inductance of Solenoid
•
L=N
N
%N2 (
Δ Φ N(B A − 0) N(µ0 l I)A
=
=
= µ0 '
*A
ΔI
(I − 0)
I
& l )
"N2 %
2
L = µ0 $
' A = µ0 n A l
# l &
€
€
•  See Example 32.1, page
929
Test question 63
•  When current decreases in time in a coil
the self-induced current tries to keep the
total current constant. Where it takes
energy for this resistance?
•  A coil with a self-inductance of 6 H has a
constant current of 2 A flowing through it
for 2 seconds. What is the emf induced in
this coil?
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Test question 64, 67
•  A coil with a self-inductance of 6.0 H is
connected to a dc source through a switch. As
soon as the switch is closed at t = 0 s, the rate
of change of current is 2.0 A/s. What is the
emf induced in this coil at t = 0 s?
•  The inductance of a solenoid 16.0 cm long
with a cross-sectional area of 1.00 × 10-4 m2
is 1.00 mH. How many turns of wire does
this solenoid have?
Energy stored in a Magnetic
Field
Pav = Vab i = L i
•  Even if R=0 battery
produces work to force
charge flow through the
inductor (Lenz’s law).
This energy is stored in
magnetic filed like the
energy of capacitor is
stored in electric field.
di
dt
dU = L i d i
I
U = L ∫ idi =
0
L I2
2
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Magnetic energy density
L = µ0 n 2 A l,
1
1
U = L I 2 = (µ0 n 2 A l) I 2
2
2
B = µ0 n I
1 2
1 2
U=
B A l ⇒ uB =
B
2 µ0
2 µ0
uE =
ε0 2
E
2
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•  Solve Example 32.3,
32.4 page 934
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The RL circuits
•  For such circuit all parameters are
functions of time.
E
L
i = (1 − e−t / τ ), τ =
R
R
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Current decay in RL circuit
•
i = I0 e−t / τ
where τ =
L
R
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Transformers
•  Transformer is
a device which
perform
voltage
conversion.
•  High voltage
power line 750,000 [V]
•  TV tube 15,000 [V]
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How it is working?
Δ ΦP
Δt
Δ ΦS
ES = − NS
Δt
EP NP
VP N P
=
⇒
=
ES NS
VS N S
N
VS = VP S
NP
EP = − NP
•  VS < VP step-down
transformer
•  VS > VP step-up
transformer
PP = PS ⇒ IP VP = IS VS
IS VP N P
=
=
IP VS N S
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€
Step-up and step-down
transformers
Step-up
Step-down
NS > NP
NS < NP
VS > VP
VS < VP
IS < IP
IS > IP
PS = PP
PS = PP
•  The primary coil of a
transformer has 100 turns
and its secondary coil has
400 turns, if the ac voltage
applied to the primary coil
is 120 V, what voltage is
present in its secondary
coil?
•  A) 100 V
•  B) 30 V
•  C) 480 V
•  D) 400 V
Test problems 78, 80
•  The primary coil of a transformer has 100 turns and its secondary coil
has 400 turns. If the ac current in the secondary coil is 2 A, what is
the current in its primary coil?
•  A) 2 A
•  B) 8 A
•  C) 1/2 A
•  D) 4 A
•  A step-up transformer doubles a primary voltage 110 V (ac). What is
the ratio of the number of turns in its primary coil to those in the
secondary coil?
•  A) 1:4
•  B) 4:1
•  C) 2:1
•  D) 1:2
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Transformer
near your
home
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