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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)

+

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