Inductance

1
Inductance

• We know that a changing magnetic flux in a loop
  induces an EMF in the loop
• If we place two loops side-by-side and change the
  current through one of the loops, an EMF will be
  induced in the other loop since the changing
  current changes the magnetic flux in the second
  loop

2
Inductance
3
Inductance

• You can use this scheme to provide power for a
  pacemaker
• Simply have an external power source that applies
  an AC voltage to an external coil
• An internal coil in the pacemaker picks up the
  induced voltage which powers the pacemaker
• You dont need an internal battery that needs to
  be replaced periodically

4
Self Inductance

• Apply an AC voltage to a single coil
• The changing magnetic field in the coil induces
  an EMF in the coil
• According to Lenzs Law this EMF will tend to
  oppose the change in magnetic field

L is called the self-inductance or just the
inductance of the coil
5
Inductance

• The inductance tends to limit the current that
  can flow in an AC circuit
• It impedes the flow of current
• Rather than talk about the resistance to the flow
  of current, we talk about the impedance
• More soon when we look at circuits

6
Long Solenoid
7
Energy Storage

• Earlier we saw that we can store energy in the
  electric field inside a capacitor
• The energy stored in the magnetic field of a coil
  carrying a current is just LI2/2
• Lets show how this plays out for the solenoid we
  just considered

8
Energy Storage
9
LR Circuit
The situation that unfolds when we connect the
voltage source to the LR circuit
10
LR Circuit
The situation that unfolds when we disconnect the
voltage source from the LR circuit
11
AC Circuits and Impedance

• We are going to consider circuits in which the
  voltage source is sinusoidal
• Well first look at resistors, capacitors and
  inductors separately
• Then well do some combining to make more
  complicated circuits
• I I0cos2?ft VrmsV0/21/2 IrmsI0/21/2

12
AC Circuits - Resistor
13
AC Circuits - Inductor
14
AC Circuits - Capacitor
15
AC LRC Circuits

• We have to package it all together
• Kirchoffs Law says the sum of the voltage drops
  around a closed loop is zero
• This is true instantaneously
• However, due to phase differences, it is not true
  for the peak or rms voltages
• The current at any instant in a series circuit is
  the same!

16
AC LRC Circuits
We make a phasor diagram to figure out phase
angles or how current leads or lags voltage
17
AC LRC Circuits
To account for the AC input voltage, we allow
the diagram to rotate counter-clockwise at 2?f
radians/sec. We are still preserving the
relationships between the phase angles of the
resistor, inductor and capacitor.
18
AC LRC Circuits
The projections of the voltage vectors on the
x-axis represent the instantaneous voltage drops
across the three circuit elements. To found out
the overall voltage from the source, we have to
make the sum of the voltage drops around the
closed loop equal zero. This means a vector
addition.
19
AC LRC Circuits
20
AC LRC Circuits
21
Resonance in AC Circuits
22
Impedance Matching

• We often have to connect one circuit to another
  circuit
• Measuring device connected to display unit such
  as oscilloscope or chart recorder, etc.
• Two cases are important
• First is to transfer maximum power
• Second is to disturb original circuit as little
  as possible

23
Impedance Matching
24
Impedance Matching

• If power transfer is not important, such as
  looking at the output of a sensor, then we need
  to make the resistance of circuit 2 as high as
  possible
• This prevents circuit 2 from having any effect on
  what is going on in circuit 1
• Power transfer is important in hooking stereo
  speakers to an amplifier