Inductors and Transformers
I.
Inductors (Review)
In the previous lesson on Faraday's Law of Magnetic Induction, we developed the
idea of inductance and inductors. We will examine these concepts in more detail
during this lesson and compare our results to our previous results with capacitors.
A.
Definition of an Inductor:
An electrical element that stores energy in a magnetic field.
"A Magnetic Piggy Bank"
The Magnetic Analog To The Capacitor
+
I
B.
VL
-
Symbol:
L
C.
Definition of Inductance:
A measure of the capacity of the inductor to store energy in a magnetic field. It
is a constant that depends only on geometry and the material inside the
inductor.
"Analogous To Capacitance"
D.
Equation Defining Inductance:
L   Total  N  B
I
I
EXAMPLE: Determine the inductance of a solenoid of radius 0.100 m and length
8.00 m with 2000 turns per meter.
SOLN:
E.
Units of Inductance:
The unit of inductance is the ____________________. The symbol is ________.
Joseph ____________ was a contemporary of Michael Faraday and the next
great physicist in American history after Benjamin Franklin. He was instrumental
in developing the physics department at Johns Hopkins and in the creation of the
Smithsonian. He also helped his friend Samuel Page setup the U.S. Patent Office.
F.
Voltage-Current Relationship:
Although it is technically incorrect to use the term voltage in connection with an
inductor since the electric force is nonconservative, the terminology is so
prevalent that it has become standard. Such misconceptions are common in other
parts of physics. People say that an object "is cold" instead of saying that the
object "is less warm." They say that an object is "pulled by the vacuum" instead
of saying that the object was "pushed by the air."
VL  L I
t
NOTE: When a constant current flows through an inductor, the inductor has a magnetic
field and therefore has stored energy. However, there is no induced emf across the
inductor!! Thus, an inductor acts like a ____________________ for DC.
NOTE: When you try to change the current through the inductor, you experience an
induced emf that opposes the change in the current. A change in the current through the
inductor causes a change in the magnetic field and thereby a change in the energy stored
in the magnetic field. Since it takes time to either remove or store energy in a system, the
current through an inductor can not be changed instantaneously just as the voltage across
a capacitor can not be changed instantaneously.
EXAMPLE: The current-time graph for an inductor is shown below. Graph the induced
emf as a function of time for the inductor.
I (A)
4
5
10
time (ms)
II.
Combining Inductors
We now consider circuits that contain several inductors in the same manner that
we considered capacitors and resistors.
A.
Inductors in Series
Placing inductors in series creates a _____________________ inductor.
I
L2
L1
LTOTAL =
B.
Inductors in Parallel
Placing inductors in parallel creates a _____________________ inductor.
I
+
VL
L2
L1
-
1
LTOTAL

L3
III.
Energy Stored In An Inductor
We already know that the power can be determined for any electrical element
using:
P=IV
For the inductor, we have that
P=
However, power is related to energy by
P  U
dt
Thus, we can find the energy in an inductor by
U =
IV.
LR Circuits
An LR circuit is a circuit in which an inductor and resistor are placed in series.
These circuits are analogous to RC circuits. In the RL circuit, the amount of
current flowing through the inductor can increase causing more energy to be
stored inside the magnetic field of the inductor or the amount of current can
decrease in which case the inductor gives up energy from its magnetic field to try
to slow the change in the current.
A.
Time Constant - 
τ=
L
R
B.
The inductor’s current CAN NOT change instantaneously (i.e. it must be
continuous). The reason for this is that the energy stored in the magnetic field
depends on the current and it always takes time to add or remove energy.
C.
After closing or opening a switch and waiting a long time, all inductors will act as
a “short circuit” (i.e. No Voltage Dropped) in an RL circuit.
D.
Close Switch
E.
Open Switch
V.
Transformers
The book covers the concept of mutual inductance for two coils in some detail. In
the lecture notes, I am only covering the special application of the mutual
inductance for two coils called a transformer. The more rigorous coverage of
mutual inductance is left for your reading.
Consider two coils as shown below where the magnetic flux produced in coil 1 for
a single loop is the magnetic flux seen by a loop in coil 2.
I2
I1
+
+
V1
V2
-
-
"N1 turns"
"N2 turns"
From Faraday's Law of Magnetic Induction, we have
V1 =
V2 =
Since the flux seen by a single loop is the same for both coils, we have that
V2 
V1
Thus, the transformer provides a way to "step up" or "step down" a time varying
voltage supply.
If N2 > N1 then the voltage is stepped up!!
If N2 < N1 then the voltage is stepped down!!
Question: What about the current?
Answer: The power provided to coil 2 is supplied by coil 1. Thus, we have that
P=
Thus, we have that
I2 
I1
Thus, if we increase the voltage we _____________________________ the current.
(conservation of energy)