9_d_Inductors_and_Inductances.pdf

Dr. Zuhair M. HejazSet 9d Magnetic Forces, Materials &

Devices1

Part IIMagnetostatic

Cont.Set 9 d (Last)

Inductors

And

InductancesDr. Zuhair M. Hejaz

Set 9d Magnetic Forces, Materials & Devices

2

Inductors And Inductances• A circuit (or closed conducting path) carrying

current produces a magnetic field which

causes

a flux

• This flux passes through

each turn of the circuit as

shown

• If the circuit has identical turns, we define the

flux linkage as . Also, the flux linkageDr. Zuhair M. Hejaz


3

Inductors And Inductancesis proportional to the current producing it, so

or

where is a constant of proportionality calledthe Inductance of the circuit.

• A circuit or part of a circuit that has inductance is called an Inductor.

• So, we can define inductance of an inductor as the ratio:

Henry ( )


Devices4

Inductors And Inductances• This last eqn. is commonly referred to as self-inductance since the linkages are produced bythe inductor itself.

• Inductance can be regarded as a measure ofhow much magnetic energy is stored in aninductor.

• The magnetic energy (in Joules) stored in aninductor is expressed in circuit theory as:

or


Devices5

Inductors And Inductances• If we have two circuits carrying current and

as shown

a magnetic

interaction exists

between the two

circuits

• Four component fluxes are produced:

• For example , is the flux passing through


Devices6

Inductors And Inductancescircuit 1 due to current in circuit 2.

• Now, we define the Mutual Inductance asthe ratio of the flux linkage on circuit 1 tocurrent , that is:

• The mutual inductance is defined as:

Note


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Inductors And Inductances• If the medium surrounding the circuits is linear

(i.e., NO ferromagnetic material):

Henry ( )

• The mutual inductance should not be confusedwith the magnetization vector expressed inAmperes/meter.

• In this case of two mutual inductors, we definethe self-inductance of circuits 1 and 2,respectively, as:

andDr. Zuhair M. Hejaz


8

Inductors And Inductances

where

and

• The total energy in the magnetic field is the sum of the energies due to , is:


Devices9

Inductors And Inductances• The positive sign is taken if currents and

flow so to strengthen the fields of each other.

• If the currents flow such that their magneticfields oppose each other, the negative sign istaken.

• Typical examples of inductors are toroids,solenoids, coaxial and parallel-wiretransmission lines.

• The self-inductance can be found by thefollowing steps


Devices10

Inductors And Inductances1. Choose a suitable coordinate system.

2. Let the inductor carry current .

3. Determine from Biot-Savart's law (or from Ampere's law if symmetry exists) and calculate from:

4. Finally find from:


Devices11

Inductors And Inductances• The mutual inductance between two circuits is

calculated by taking a similar procedure.

• Note that, the total energy stored in amagnetostatic field in a linear medium is:

• Which is similar to that for an electrostatic field:


Devices12

Example Applications• Coaxial Cable Inductance:

• Applying the eqn. to that derived in

the previous chapter for the total flux for a length and :

• So, the inductance is

• Or on a per meter basis (unit length)


Devices13

Example Applications

• Toroidal Coil Inductance: The total flux for N turns and a current is:

where is the

cross section area.

• Now, multiplying the total flux by , we get theflux linkage, then dividing by , we get:

The inductance


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You have learned


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• That the inductance of a structure is proportionalto the flux linkage .

• That the flux linkage is proportional not only tothe number of turns ( ) generating the flux butalso to the number of turns intercepting this flux.

• That the self inductance of a coil is proportionalto .

• How to calculate the inductance per unit lengthof various transmission lines.

Some Suggested Problems

• Some Suggested Problems (Text Book Ch. 9)

• Solve the following problems:

• 9. 36, 9.37, 9.38, 9.41


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End of Set 9 d

End of CourseWish you the best in your

final exams


Devices17

9_d_Inductors_and_Inductances.pdf

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