ECE 3336 Introduction to Circuits & Electronics Note Set #7b Inductors Fall 2012, TUE&TH 4:00-5:30pm Dr. Wanda Wosik

Current Can Generate Magnetic Field From Amper law Hans Christian Oersted (1777-1851) r

Magnetic Field Generated by Current Loop Superposition of the magnetic fields from the loops creates a uniform B field in the coil = solenoid N S Solenoid http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfie.html#c1

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

Moving Charges and Magnetic Forces Wires w/ current placed in the magnet feel force moves Faraday’s Law of Induction + - Wire w/o current moved () in the magnet  Charges forced to move=current Voltage generate + -  http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magint.html#c1

1. 2. 3. 4. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/farlaw.html#c1

Faraday’s Law  Lenz’s Law 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 Lenz’s Law Directions of Voltages N S N S S N S N http://hyperphysics.phy-astr.gsu.edu/hbase/electric/farlaw.html#c2

Inductors in Circuits  Emf applied Define INDUCTANCE L  So the Emf gives us voltage of an opposite sign than the applied voltage V(t) http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/indcur.html#c2 EXAMPLE http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/coilbulb.html#c1

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.

Transients in Inductors http://hyperphysics.phy-astr.gsu.edu/hbase/electric/indtra.html#c1

Polarities of Inductors  None 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. And as for resistor, the voltage and current directions follow the passive (or active) sign convention. Passive Sign Convention Active Sign Convention

Voltage vL≠0 only if iL=f(t) Ideal inductor does not have resistance Finding Currents in Inductors  Voltage vL≠0 only if iL=f(t) Ideal inductor does not have resistance s is dummy variable Initial conditions They do not produce voltage vL But the energy is stored

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

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. 

Series Inductors Equivalent Circuits Series inductors, L1 and L2… and Ln, can be replaced with an equivalent circuit with a single inductor LEQ iLEQ From KVL:  (∑Li is as for resistors)

Parallel Inductors Equivalent Circuits Parallel inductors, L1 and L2 …Ln, can be replaced with an equivalent circuit inductor LEQ + vL(t) - iL1\2(t) iLn(t) iL1(t) iLEQ(t)  LEQ Use KCL As for resistors ∑(1/Ri) 

Rules for Inductors Passive sign convention

Some Applications: Electric Motors AC operation DC operation http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/motdc.html#c1

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

Mutual Inductance and Transformers

Transformers Number of turns in primary and secondary coils important More on Transformers in Note Set #16