Lesson 21 - Inductors and RL Circuits

restmushroomsElectronics - Devices

Oct 7, 2013 (3 years and 9 months ago)

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Lesson 21
-

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




B.

Symbol:






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:






+

I

-

V
L

L

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 help
ed 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

pr
evalent 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 tha
t the object was "pushed by the air."






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 c
apacitor 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.


















time (ms)

I (A)

4

5

10

II.

Combining Inductors



We now co
nsider 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.










L
TOTAL

=





PROOF:























L
1

L
2

I

B.

Inductors in Parallel



Placing inductors in parallel creates a _____________________ inductor.























PROOF:





















L
1

L
2

L
3

I

+

-

V
L

III.

Energy Stored In An Inductor



We already
know that the power can be determined for any electrical element

using:


P = I V



For the inductor, we have that





P =




However, power is related to energy by





Thus, we can find the energy in an inductor by


























U =

IV.

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 tra
nsformer. 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.













"N
1

turns"




"N
2

turns"




From Faraday's Law of Magnetic Induction, we have





V
1

=





V
2

=





Since the flux seen by a single loop is the same for both coils, we have that











Thus, the transformer provides a way t
o "step up" or "step down" a time varying

voltage supply.

I
1

V
1

-

+

I
2

+

-

V
2


If N
2

> N
1

then the voltage is stepped up!!



If N
2

< N
1

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









Thus, if we increase the voltage we _____________________________ the current.



(conservation of energy)