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

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Equivalent Inductance

In series

In parallel

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Growth of current in an Inductive Circuit

R

LV v Li

++

-

tL

R

tL

R

e1R

Vi

R

Ve

R

Vi

R

VA

R

VA0

0i0;tAt

:

R

VAei

R

Vi

L

Vi

L

RPI

PIAei

L

Vi

L

RD

Ridt

diLV

tL

R

PI

tL

R

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Growth of current in an Inductive Circuit …

Time Constant, = L/RTime taken by the current through the inductor to reach its final steady state value, had the initial rate of rise been maintained constant

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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

ab

i LA

i0;tAt

0

0

0

0

I

I

PI

PIAei

Ridt

diL

tL

R

tL

R

0

L

tL

R

0

tL

R

0

tL

R

0

e

0V

ee

ei

VV

V

VRIV

I

L

R

R

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Decay of current in an Inductive Circuit …

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Energy stored in an Inductor

2

0

Instantaneous power,

Energyabsorbed during is

Energyabsorbed by the magnetic field when current isincreased from to

A is

Jou

0

les

I

1

2

L

I

dip v i L i

dtdt

dw Lidi

W Li di L I

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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

0 .1 H

1 5

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 -(R1

t/L) = 0.632 e-250(t – 0.01)