Elec-Lec4

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prepared by ZAIN RAZA

INDUCTORS

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Inductors

An inductor is a coil of wire through

which a current is passed. The

current can be either AC or DC.

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Induction Forming

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For a constant current, the inductor behaves

as a piece of wire, so it will act as a small

resistance. For a current whose value varies with time

new things start to happen. When the

current varies, the two terminals of an

inductor start to show a voltage diff. V,

V is proportional to the rate of current

change: di/dtV = L di/dt

NOTE: When current is varied in a straight wire, negligible PD

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dt

dILV

L

L!

Varying Current

generates a

magnetic field B,

Which induces a

voltage proportional

to the rate of change

of the current.

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An other way defining INDUCTANCE

The ability of an inductor to storeenergy in the form of a magnetic field(and consequently to oppose changesin current) is called inductance.

Energy stored in L:

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Current flow in an inductor creates

a magnetic field inside theloops and partly also on the outside

and this magnetic field stores

energy. The stored energyprevents the current from

changing too quickly. Conversely,

when the current tries to stop,energy stored in the magnetic field

will try to maintain it, so it cannot

decline too fast.

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The behavior of an inductor in acircuit is like a turbine driving a

flywheel. The turbine is assumed tobe frictionless device. A heightdifference between the inlet and

the outlet of the turbine drives theflywheel.

If the waterlevels in front of the

turbine and behind the turbine aresuddenly madeequal, themomentum of the flywheel will try

to keep the water current flowing.

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If the resistance of the coil is very small,

the alternating voltage across the coil

leads the current by 90 degrees (in the

opposite direction to that in a capacitor).

Fig in next slide:

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If the resistance of the coil is very small,

the alternating voltage across the coil

leads the current by 90 degrees (in the

opposite direction to that in a capacitor).

Fig in next slide:

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In addition to the ordinaryresistance of its wire, inductor has

another 'resistance-like property,effective only for AC currents,called the inductive reactance.

The inductive reactanceXL is the

ratio of the peak voltage

amplitude to the peak current

amplitude, X = Vp / IpL

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The reactance remains

constant for a fixed frequency,but its value is frequency

dependent: X= w L

L

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The inductance will tend tosmooth sudden changes in

current just as the capacitancesmoothes sudden changes involtage. Of course, if the currentis constant there will be noinduced EMF. So unlike the

capacitor which behaves like anopen-circuit in DC circuits, aninductor behaves like a short-

circuit in DC circuits.

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Combining Inductors

Inductances add like resistances

Series

Parallel

L L L LN

! 1 2

...

1 1 1 1

1 2 L L L L

N

! ...

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Inductor Impedance

Note that this behavior is exactly the oppositeof capacitors.

frequencyfrequency

approaches

impedance

approacheslooks like called

low zero zero short circuit

high infinity infinity open circuit

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Transformers

Cylinders (solenoids)

Toroids

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Some Interesting Transformers

A huge range in sizes

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Some Interesting Transformers

High Temperature Superconducting Transformer

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Transformers

Note that for a transformer, the symbol

shows two inductors. One is the primary

(source end) and one is the secondary

(load end): LS& LL

The inductors work as expected, but theyalso couple to one another through their

mutual inductance: M2=k2LSLL

Symbol for

transformer

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Transformers

The voltages across the primary and

secondary terminals of the transformer arerelated by

Note that the coil with more turns has the

larger voltage

N V N V S L L S

!

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