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Inductor
ELE 101 / 102 Dept of E & E Engg, MIT Manipal 2
Inductor
Inductor is a passive electric device that store energy in its
Magnetic field when a current flows through it
A coil of wire wound on a Ferromagnetic core
Air core Inductor, iron core inductor
Circuit representation is
ELE 101 / 102 Dept of E & E Engg, MIT Manipal 3
Inductive Circuit
Inductance (L) : Property which opposes the rate of
change of current.
The voltage induced in the inductor is proportional to the rate of
change of current flowing through it
eL = L (di/dt)
Unit is Henry (H).
This proportionality constant is the self inductance or
inductance (L)
L
+
i vL
ELE 101 / 102 Dept of E & E Engg, MIT Manipal 4
Equivalent Inductance
In series
In parallel
ELE 101 / 102 Dept of E & E Engg, MIT Manipal 5
Growth of current in an Inductive Circuit
R
LV v Li
+
+
-








−=
+−=∴
−=⇒+=
==
+=
=






=
+=
=





+
+=






−






−





−






−
t
L
R
t
L
R
e1
R
V
i
R
V
e
R
V
i
R
V
A
R
V
A0
0i0;tAt
:
R
V
Aei
R
V
i
L
V
i
L
R
PI
PIAei
L
V
i
L
R
D
Ri
dt
di
LV
t
L
R
PI
t
L
R
ELE 101 / 102 Dept of E & E Engg, MIT Manipal 6
Growth of current in an Inductive Circuit …
Time Constant, τ = L/R
Time taken by the current through the inductor to reach its final
steady state value, had the initial rate of rise been maintained
constant
ELE 101 / 102 Dept of E & E Engg, MIT Manipal 7
Decay of current in an Inductive Circuit …
Initial current is through inductor is I0 = V/R
At t =0, switch is moved from position a to b
R
V
t = 0
a
b
i LA
i0;tAt
0
0
0
0
=
==
=
+=
=+






−
I
I
PI
PIAei
Ri
dt
di
L
t
L
R
t
L
R
0
L
t
L
R
0
t
L
R
0
t
L
R
0
e
0V
ee
ei






−






−





−






−
−=∴
=+
==
=∴
VV
V
VRIV
I
L
R
R
ELE 101 / 102 Dept of E & E Engg, MIT Manipal 8
Decay of current in an Inductive Circuit …
ELE 101 / 102 Dept of E & E Engg, MIT Manipal 9
Energy stored in an Inductor
2
0
Instantaneous power,
Energyabsorbedduring is
Energyabsorbed by the magnetic field when current is
increased from to A is
Jou
0
les
I
1
2
L
I
di
p v i Li
dt
dt
dw Lidi
W Li di L I
= =
=
= =∫
ELE 101 / 102 Dept of E & E Engg, MIT Manipal 10
Example
In the network shown in figure, the switch is closed to position 1 at t = 0 and is
moved to position 2 at 10 ms. Determine iL(t) & sketch it.
1 0 V
1 0 Ω
0 . 1 H
1 5 Ω
t = 1 0 m s
1 2
Switch in 1; for 0≤ t ≤ 10 ms
i1 (t) = (V/R) * (1 – e -(R t/L)
) = 1- e -100 t
At ‘t’ = 10 ms; I1 = 0.632 A
Switch in 2; t > 10 ms
i2 (t) = I1 * e -(R
1
t/L)
= 0.632 e-250(t – 0.01)

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L6 inductor

  • 2. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 2 Inductor Inductor is a passive electric device that store energy in its Magnetic field when a current flows through it A coil of wire wound on a Ferromagnetic core Air core Inductor, iron core inductor Circuit representation is
  • 3. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 3 Inductive Circuit Inductance (L) : Property which opposes the rate of change of current. The voltage induced in the inductor is proportional to the rate of change of current flowing through it eL = L (di/dt) Unit is Henry (H). This proportionality constant is the self inductance or inductance (L) L + i vL
  • 4. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 4 Equivalent Inductance In series In parallel
  • 5. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 5 Growth of current in an Inductive Circuit R LV v Li + + -         −= +−=∴ −=⇒+= == += =       = += =      + +=       −       −      −       − t L R t L R e1 R V i R V e R V i R V A R V A0 0i0;tAt : R V Aei R V i L V i L R PI PIAei L V i L R D Ri dt di LV t L R PI t L R
  • 6. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 6 Growth of current in an Inductive Circuit … Time Constant, τ = L/R Time taken by the current through the inductor to reach its final steady state value, had the initial rate of rise been maintained constant
  • 7. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 7 Decay of current in an Inductive Circuit … Initial current is through inductor is I0 = V/R At t =0, switch is moved from position a to b R V t = 0 a b i LA i0;tAt 0 0 0 0 = == = += =+       − I I PI PIAei Ri dt di L t L R t L R 0 L t L R 0 t L R 0 t L R 0 e 0V ee ei       −       −      −       − −=∴ =+ == =∴ VV V VRIV I L R R
  • 8. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 8 Decay of current in an Inductive Circuit …
  • 9. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 9 Energy stored in an Inductor 2 0 Instantaneous power, Energyabsorbedduring is Energyabsorbed by the magnetic field when current is increased from to A is Jou 0 les I 1 2 L I di p v i Li dt dt dw Lidi W Li di L I = = = = =∫
  • 10. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 10 Example In the network shown in figure, the switch is closed to position 1 at t = 0 and is moved to position 2 at 10 ms. Determine iL(t) & sketch it. 1 0 V 1 0 Ω 0 . 1 H 1 5 Ω t = 1 0 m s 1 2 Switch in 1; for 0≤ t ≤ 10 ms i1 (t) = (V/R) * (1 – e -(R t/L) ) = 1- e -100 t At ‘t’ = 10 ms; I1 = 0.632 A Switch in 2; t > 10 ms i2 (t) = I1 * e -(R 1 t/L) = 0.632 e-250(t – 0.01)