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

2. Current Can Generate Magnetic Field
From Amper law
Hans Christian Oersted
( ) r

3. 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

4. Lorentz Force Law Moving Charges
Rotate
I towards B
Wires carrying currents will experience forces

5. 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 + - 

6. 1. 2. 3. 4.

7. 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

8. Inductors in Circuits  Emf applied Define INDUCTANCE L 
So the Emf gives us voltage
of an opposite sign than the applied voltage V(t)
EXAMPLE

9. 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.

10. Transients in Inductors

11. 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

12. 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

13. 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

14. 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. 

15. 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)

16. 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) 

17. Rules for Inductors
Passive sign convention

19. Some Applications: Electric Motors
AC operation
DC operation

20. 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

21. Mutual Inductance and Transformers

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