Transcript Inductance - Wellington High School

Answers:
 The solenoid, when viewed from above, has a clockwise current in
it. This means that the top of the solenoid is forming a magnetic
south pole.
Lenz’s law states that the induced current must create a force that
opposes the force that caused the current. Therefore the magnetic
south of the permanent magnet must be approaching the solenoid
(i.e. the solenoid is repelling the magnet).
 The magnetic field due to the current in the wire is into the page
above the wire (use RH grip rule). The current induced in the
dropping loop must be such as to produce a magnetic field into
the page below the loop (again, to create the repulsion required by
Lenz’s law). This means that the current in the loop must be
counter-clockwise.
DC Electricity
 Internal resistance
 Kirchhoff’s rules
 Capacitors
 EM induction
 Today: Inductance
 self-inductance
 Mutual inductance
Review:
 Last time:
 The rate of change of flux is equal to the electro-motive force
(voltage) induced in a conducting loop within a changing
magnetic field.

 
t
Inductance
Mutual Inductance
Self Inductance
Energy Stored in an Inductor
Mutual Inductance.
 Transformers operate by mutual inductance.
 Mutual inductance occurs when changing the current in one
coil produces an induced voltage in another coil.
Mutual Inductance (definition)
 Demonstration (from last time)
 The magnetic flux in the second coil is
I
  (constant) I
proportional to the current in the first
coil.
 The proportionality constant is called the
mutual inductance (symbol M, unit
henry, H), so:
  M I
Mutual Inductance and Induced Voltage
 Faraday’s law states that:
 
V
t
 (M  I )

t
 Substituting Φ = M × I
 As M is a constant, and therefore
does not change:
 MI
V
t
V is the induced voltage in coil 2
ΔI is the change in current in coil 1
Δt is the time taken for the change in
current to take place
M is the mutual inductance
Practice Problem:
 Two coils are arranged so that the flux in one passes into the
other. When the current in coil 1 is increased from 0 to 5.0A
in 2.0 seconds, an induced voltage of 100 mV (0.10 V) is
induced in coil 2.
 Calculate the mutual inductance between the coils.
Self Inductance
 When a coil is connected to a supply, the current builds up to its
steady value over a time.
 Because of this, there is a changing magnetic flux in the coil.
 This change causes a voltage to be induced in the coil itself.
 For examples: read pages 249-251 in new study guide or 296-297 in
old study guide.
Inductors
 An inductor produces a voltage when the current changes.
 When an inductor is placed in a circuit, the current takes
longer to build up to maximum, or shorter to fall to zero.
 Circuit symbol:
Inductance (definition)
The effect of an inductor is measured by its self-inductance
 The flux in the inductor is proportional to the
current, I.
 The proportionality constant is called the self-
inductance, L (measured in henrys, H).
  (consant) I
  L I
 
V
 We can use Faraday’s law to find the equation
relating the inductance to the induced voltage in
the coil:
t
I
V  L
t
Inductance: Points
 Inductors only affect circuits while the current is changing
 AC circuits
 DC circuits when they are turned on or off
 Negative sign in formula shows that the induced voltage
opposes the change of currrent.
Energy in an Inductor:
 A voltage source connected to an inductor has to do work against the
inductor to create a steady current. This work is converted into potential
energy stored in the inductor.
 The equation for the energy stored in the
inductor is:
1 2
E  LI
2
 Complete activity 15C:
 Achieved: 1, 4
 Merit: 2, 5
 Excellence: 3 b
 Exam Questions
 Next lesson: Voltage and current graphs for inductors in a DC
circuit – the build-up and decay of current in inductors function in
the same way as the build-up and decay of voltage in capacitors.