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Transcript of Electromagnetism-Inductance
Two inductors have equal inductance but A has a core 2x longer than B.
How could this be true?
Inductors with Coupled Cores
Coupling = magnetic field shared between the coils
Analogy to Electric circuits:
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
A is half area of B
opposition to current change decreases
-> Inductance decreases
Connect a 5mH, 10mH, and 20mH inductor to make a total of 8.6 mH
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:
Magnetic reluctance changes with magnetic field density.
1. Magnetic flux in each coil
2+ coils wound on the same core
-> Reluctance equal
2. Core material & dimensions equal
-> mmf equal
N I =
What factors are equal?
Conservation of energy principle:
coil 1 power...
= coil 2 power
V I =
Design a transformer
V = 230 V
N = 150
V = 24 V
N = ?
= 1000 W
Core dimensions, material?
Sketch with all data shown
Swap with your neighbour to check.
cassette / VHS tapes
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
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.
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?
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.
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?
The coil must oppose the external action
-> Magnet moving in must be
-> Magnet moving away must be
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
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
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