1 ece 3336 introduction to circuits & electronics note set #7b inductors fall 2012, tue&th...
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ECE 3336 Introduction to Circuits & Electronics
Note Set #7bInductors
Fall 2012,TUE&TH 4:00-5:30pmDr. Wanda Wosik
Current Can Generate Magnetic Field
Hans Christian Oersted(1777-1851)
From Amper law
r
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Magnetic Field Generated by Current
Loop
Solenoid
Superposition of the magnetic fields from the loops creates a uniform B field in the coil = solenoid
N S
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfie.html#c1
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Lorentz Force Law Moving Charges
Rotate I towards B Wires carrying
currents will experience forces
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfor.html#c2
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Moving Charges and Magnetic Forces
Wire w/o current moved () in the magnetCharges forced to move=currentVoltage generate +
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Faraday’s Law of Induction
Wires w/ current placed in the magnet feel force moves
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magint.html#c1
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1.
4.
2.
3.
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/farlaw.html#c1
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Electromagnetic induction produces current in a conductor, which is being moved in the magnetic field.
That creates a magnetic field in a coil opposing any change of original magnetic field VOLTAGE
Faraday’s Law Lenz’s Law
Lenz’s Law Directions of VoltagesN S N S
S N S N
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/farlaw.html#c2
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Inductors in Circuits
applied Define INDUCTANCE L
So the Emf gives us voltage
of an opposite sign than the applied voltage V(t)
Emf
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/indcur.html#c2
EXAMPLEhttp://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/coilbulb.html#c1
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Inductors
Inductance is present in wires whenever ac currents flow and ac magnetic fields are produced.
The ac current produces a voltage, which counteracts the changes of this current
Fast changes of currents i.e. high frequency signals result in high opposing voltages; that leads to very low currents making the inductor to appear as an open circuit.
The energy stored In magnetic fields has effects on voltage and current. We use the inductor component to model these effects.
Chokes – used for high inductance i.e. it will block high frequency signals.
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Transients in Inductors
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/indtra.html#c1
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Polarities of Inductors None
And as for resistor, the voltage and current directions follow the passive (or active) sign convention.
Unlike reference polarities of current sources and voltages sources, there is no polarity to an inductor. Just like in resistors: there was no polarities, either.
Active Sign ConventionPassive Sign Convention
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Finding Currents in Inductors
s is dummy variable
• Initial conditions
• They do not produce voltage vL
• But the energy is stored
Voltage vL≠0 only if iL=f(t)
Ideal inductor does not have resistance
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Current Change is Limited so is the Voltage
• The current through an inductor cannot be changed instantaneously.
• This would make the voltage infinite - but large voltages can be produced.
and
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Energy in Inductors
We can find the energy stored in the magnetic field associated with the inductor. Start with power find energy.
Integration limits: when the current is zero no magnetic field no energy stored
• So lower limit=0; • The upper limits set by the value of current, iL.
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Series Inductors Equivalent Circuits
Series inductors, L1 and L2… and Ln, can be replaced with an equivalent circuit with a single inductor LEQ
(∑Li is as for resistors)
iLEQ
From KVL:
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Parallel Inductors Equivalent Circuits
Parallel inductors, L1 and L2 …Ln, can be replaced with an equivalent circuit inductor LEQ
Use KCL
As for resistors ∑(1/Ri)
LEQ
iL1(t)iL1\2(t) iLn(t) iLEQ(t)
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vL(t)
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Rules for Inductors
Passive sign convention
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Some Applications: Electric Motors
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DC operationAC operation
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/motdc.html#c1
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Mutual Inductance (M)
“M” describes how current in one coil induces the current/voltage in the second coil.
This concept will be used in Transformers
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Mutual Inductance and Transformers
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Transformers
Number of turns in primary and secondary coils important
More on Transformers in Note Set #16