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Transcript of 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
Set 9d Magnetic Forces, Materials & Devices
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 ( )
Dr. Zuhair M. HejazSet 9d Magnetic Forces, Materials &
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
Dr. Zuhair M. HejazSet 9d Magnetic Forces, Materials &
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
Dr. Zuhair M. HejazSet 9d Magnetic Forces, Materials &
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
Dr. Zuhair M. HejazSet 9d Magnetic Forces, Materials &
Devices7
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
Set 9d Magnetic Forces, Materials & Devices
8
Inductors And Inductances
where
and
• The total energy in the magnetic field is the sum of the energies due to , is:
Dr. Zuhair M. HejazSet 9d Magnetic Forces, Materials &
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
Dr. Zuhair M. HejazSet 9d Magnetic Forces, Materials &
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:
Dr. Zuhair M. HejazSet 9d Magnetic Forces, Materials &
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:
Dr. Zuhair M. HejazSet 9d Magnetic Forces, Materials &
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)
Dr. Zuhair M. HejazSet 9d Magnetic Forces, Materials &
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
Dr. Zuhair M. HejazSet 9d Magnetic Forces, Materials &
Devices14
You have learned
Dr. Zuhair M. HejazSet 9d Magnetic Forces, Materials &
Devices15
• 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
Dr. Zuhair M. HejazSet 9d Magnetic Forces, Materials &
Devices16
End of Set 9 d
End of CourseWish you the best in your
final exams
Dr. Zuhair M. HejazSet 9d Magnetic Forces, Materials &
Devices17