**Electro-Magnetism**

**Inductors**

Puzzle...

Two inductors have equal inductance but A has a core 2x longer than B.

How could this be true?

**Combining Inductors**

Series

Inductors with Coupled Cores

Coupling = magnetic field shared between the coils

eg. Transformer

Magnetic Circuits

Analogy to Electric circuits:

Magnetic Memory

Applications for magnetism require strong magnetic memory or weak:

Core material permeability:

A is half value of B

Number of turns:

A has 0.707 x B turns

Core Area:

A is half area of B

Parallel

Current

Voltage

opposition to current change decreases

-> Inductance decreases

Connect a 5mH, 10mH, and 20mH inductor to make a total of 8.6 mH

Mutual Inductance

One changing magnetic field causes a current in a second coil.

Simplified if air-core:

M also in Henries.

Add / subtract from series inductance total.

Coupling Coefficient ratio:

Perfect transformer:

k =

1.0

Magnetic reluctance changes with magnetic field density.

Transformers

1. Magnetic flux in each coil

2+ coils wound on the same core

-> Reluctance equal

2. Core material & dimensions equal

-> mmf equal

N I =

1

1

N I

2

2

What factors are equal?

Conservation of energy principle:

coil 1 power...

= coil 2 power

V I =

1

1

V I

2

2

Design a transformer

Primary

V = 230 V

N = 150

Secondary

V = 24 V

N = ?

Power limit

= 1000 W

Combined Ratio:

Currents?

Core dimensions, material?

mmf?

Mag Flux?

Flux density?

Core saturated?

Sketch with all data shown

Swap with your neighbour to check.

'Hard' materials

'Soft' materials

'permanent' magnets

computer disks

cassette / VHS tapes

AC motors

transformers

Hysteresis causes losses when reversing the magnetic field

Changing Magnetic Fields

Self-induction / mutual-induction

A coil will generate a voltage whenever it experiences a changing magnetic field

Faraday's Law

Michael Faraday is credited with this relationship between a changing magnetic field and the coil's voltage.

Lenz's Law shows that the generated voltage and current always opposes the field which created it.

Exercise:

A 50 Hz current creates an alternating magnetic field in a transformer core.

The peak intensity of the magnetic flux is 5 mWb (fluctuating as a sine wave).

How many turns are needed on the secondary winding to produce a maximum of 48 V?

Solution:

rate of change of flux... differentiate!

maximum=amplitude of differentiated sine function

= 0.005 x 2 x pi x 50 = 1.57 Wb/s

Now solve for N

48V = N. 1.57

N = 31

Rotating Magnet + Coils

A magnet rotates past three independent coils.

Each coil will generate a maximum voltage whenever it experiences

-> 120 deg phase shift.

3-phase power!

The peak of each voltage occurs at different times.

If evenly spaced...

Hampson & Hanssen, Electrical Trade Principles, p216.

...a fast-changing magnetic field.

Lenz's law for Magnets & Coils

Does the coil attract or repel the magnet?

Attracted

Repelled

The coil must oppose the external action

-> Magnet moving in must be

-> Magnet moving away must be

Exercise:

A 'perfect' transformer has two coils of N=100 and N=50,

with a common core material, 500x250mm with permeability

of 25 mH/m. Each coil is wound with copper wire 1 mm2, resistivity 1.68x10^-8 ohm-metres.

1 What is the inductance of each coil?

2 What is the Mutual Inductance for the 'perfect' transformer?

3 What is the total resistance of each coil?

4 What is the impedance of the primary coil if 230V 50Hz was applied?

opposition to current change increases

-> Inductance increases

is the same

adds

Current

Voltage

is shared

is equal

Transients

Inductors don't "like" their current to change, because that changes the magnetic field.

-> Voltage created to oppose any change.

Time is required to reach steady-state current

V = L di/dt

eg. Testing a transformer with DC

R = 0.5 ohm L = 4H V=12V dc

1. Steady-state current

2. Time constant

3. Current after one time constant

4. Time to reach steady-state

T

= L/R

Transistor: t=50 us V(sat) = 0V

Supply: V = 12 V dc

Coil: R = 100 ohm L = 250mH

[Assume that current drops to zero linearly]

Transisitor switching a relay coil

1. Sketch this circuit

2. Steady-state current

3. Coil Voltage when transistor switches off

Sketch a sine wave current

Identify the maximum rate of change points (+/-)

Identify the zero rate of change points

What does this show about leading/lagging?

Sketch a Voltage curve to join these points

V = X = j 2 pi f L

I