Transcript Goal: To understand

Goal: To understand uses for
induction
Objectives:
1) To learn how to use Lenz’s Law to
determine the direction of an induced
current or magnetic field
2) To learn how to use Transformers
3) To learn about Inductors
4) To be able to calculate the Energy stored
inside an inductor
5) To learn about LR circuits
Lenz’s Law
•
•
V = - N Δ Φ / Δt
This is for a coil.
•
•
If the magnetic field decreases then we will produce a positive EMF.
An increase in the magnetic field likewise will produce a negative EMF.
•
The magnetic field induced from the EMF produces a magnetic flux which
counteracts the change in magnetic flux!
•
So, when the magnetic field increases (in the + direction) you induce a
negative magnetic flux from the current which gives a clockwise current.
•
A decreasing magnetic field (in the + direction) induces a counter-clockwise
current (which produces a positive magnetic flux).
•
Note: if you change a negative magnetic field then you have to notice that
an increased magnitude is really decreasing the magnetic field.
•
Bottom line is find the current which produces a magnetic field which offsets
the change in the magnetic field.
Example:
• From HW 6:
• A coil rests upright on your desk.
• A magnetic field which is at a 90 degree angle to your
desk causes a clockwise current in the coil.
• What must be true about the direction and magnitudes of
the magnetic field?
• 1) upwards from desk and increasing with time
• 2) upwards from desk and constant with time
• 3) downwards toward desk and increasing in magnitude
with time
• 4) downwards from the desk and constant with time
Example:
• From HW 6:
• A coil rests upright on your desk.
• A magnetic field which is at a 90 degree angle to your
desk causes a clockwise current in the coil.
• What must be true about the direction and magnitudes of
the magnetic field?
• 1) upwards from desk and increasing with time
• Constant magnetic field will not induce current!
• A clockwise current induces a negative magnetic flux.
• Since this is opposite to the change (to try to counteract)
that means the field must be increasing.
• The downwards one was only increasing in magnitude…
A larger negative value is actually lower…
Yesterday we saw:
• V = - N Δ Φ / Δt
• This is for a coil.
•
•
•
•
•
Imagine you had 2 coils.
The first coil would affect the 2nd coil!
So, V1 = - N1 Δ Φ / Δt
And: V2 = - N2 Δ Φ / Δt
Since Δ Φ / Δt is the same for both coils then you get
that:
• V1/V2 = N1 / N2
• This is a transformer!
Transformers
• Transformers transform 1 voltage to another.
• For example high voltage power lines carry large
amounts of energy long distances.
• They do this to save on losses.
• Then, they transform that from 100k volts to the
120 volts you use in your home using a series of
transformers.
Current in transformer
• You cannot gain energy – so the energy you get
in one is the same as the other.
• Therefore the powers are also the same!
• So, P1 = P2
• Since P = IV therefore
• I1V1 = I2V2 (or I1/I2 = V2/V1)
• Since V2/V1 = N2/N1, therefore, I1/I2 = N2 / N1
• When you shrink the voltage you increase the
current and visa versa.
Sample
• A 120k voltage line carries 0.1 A of current.
• This line is passed through a transformer.
• The high voltage end has 3000 loops and the
low end has 3 loops. After the 3 loops is a
simple light bulb.
• A) What is the power that is passed through the
receiver to the light bulb?
• B) what is the current which the light bulb
receives?
• C) What is the voltage across the 3 loop
transistor?
Transformer types
• There are 2 types of transformers:
• Step up transformers – these step up the
voltage (and decrease the current).
• These start with a small # of loops and the
other end has a large # of loops.
• If you reverse the step up transformer then
you have a step down transformer.
• These start with a large # of loops and end
up with a small # of loops – and decrease
the voltage while increasing current.
Inductors
• Inductors are the magnetic equivalent to
the electric fields capacitor.
• Just like capacitors store electric energy
Inductors store magnetic energy.
• Capacitance was how effectively you
could store charge, and Inductance is how
well you can store a magnetic field.
• So, inductance (denoted as L) is:
• L = N Φ/ I (l here is length)
Equations
• An inductor with length l and having N turns has
inductance of:
• L = μ0 N2 πr2 / l
• And the emf in a coil is just
• V = - N Δ Φ / Δt = - L Δ i / Δt
• And the power going through the inductor is:
• P = V i where i is the current at some point in
time and I is the final current.
• The average power is:
• Pav = ½ Vi
Energy in an inductor
• U = ½ Li2
• And in a circuit inductors add up the same
way as resistors.
LR circuits
• We saw RC circuits now we have LR
circuits.
• Again we have a time constant.
• However, this time τ = L/R
• Everything else is the same as for RC
circuits.
• No examples here, we are out of time!
Conclusion
• We saw with Lenz’s law that a change in
magnetic field will induce a current such that the
induced current will induce a magnetic flux to
counteract the change in magnetic field.
• We learned about transformers and saw that
while power is constant that we drop/raise
voltage and raise/drop current depending on
whether we have less/more loops on the end we
are transferring to.
• We learned about inductors.
• We saw the energy stored in an inductor and
inductors in LR circuits.