Mathematics Mathematics
in Electricity
in Electricity
By: HAZADOUS GEMS4
By: HAZADOUS GEMS4
Mat
hem
atic
s in
Mat
hem
atic
s in
E
lect
roni
csE
lect
roni
cs
Mathematics in Electronics
Mathematics in Electronics
Electrical Engineering usually include
Electrical Engineering usually include
CalculusCalculus (single and
(single and multivariablemultivariable), ),
Complex Analysis
Complex Analysis, , Differential Equations
Differential Equations (both ordinary
(both ordinary
and partial), Linear Algebra and
and partial), Linear Algebra and
Probability. Fourier Analysis and Z-
Probability. Fourier Analysis and Z-
Transforms are also subjects which are
Transforms are also subjects which are
usually included in electrical
usually included in electrical
engineering programs.
engineering programs.
Of these subjects, Calculus and
Of these subjects, Calculus and
Differential equations are usually
Differential equations are usually
prerequisites for the Physics courses
prerequisites for the Physics courses
required in most electrical
required in most electrical
engineering programs (mainly
engineering programs (mainly
Mechanics, Electromagnetism &
Mechanics, Electromagnetism &
Semiconductor Physics). Complex
Semiconductor Physics). Complex
Analysis has direct applications in
Analysis has direct applications in
Circuit Analysis, while Fourier Analysis
Circuit Analysis, while Fourier Analysis
is needed for all Signals & Systems
is needed for all Signals & Systems
courses, as are Linear Algebra and Z-
courses, as are Linear Algebra and Z-
Transform.Transform.
Ele
ctri
cian
’s M
aths
Ele
ctri
cian
’s M
aths
Intr
oduc
tion
Intr
oduc
tion
Numbers can take different forms:
Numbers can take different forms:
Whole numbers: 1, 20, 300, 4,000, 5,000
Whole numbers: 1, 20, 300, 4,000, 5,000
Decimals: 0.80, 1.25, 0.75, 1.15
Decimals: 0.80, 1.25, 0.75, 1.15
Fractions: 1/2, 1/4, 5 8, 4 3 ⁄ ⁄
Fractions: 1/2, 1/4, 5 8, 4 3 ⁄ ⁄
Percentages: 80%, 125%, 250%, 500%
Percentages: 80%, 125%, 250%, 500%
You’ll need to be able to convert these
You’ll need to be able to convert these
numbers from one form to another and
numbers from one form to another and
back again, because all of these
back again, because all of these
number forms are part of electrical
number forms are part of electrical
work and electrical calculations.
work and electrical calculations.
You’ll also need to be able to do some
You’ll also need to be able to do some
basic algebra. Many people have a
basic algebra. Many people have a
fear of algebra, but as you work
fear of algebra, but as you work
through the material here you’ll see
through the material here you’ll see
there’s nothing to fear.
there’s nothing to fear.
WH
OLE
NU
MBE
RS
WH
OLE
NU
MBE
RS
Whole numbers are
Whole numbers are exactly what the term
exactly what the term implies. These numbers
implies. These numbers
don’t contain any
don’t contain any fractions, decimals, or
fractions, decimals, or percentages. Another
percentages. Another name for whole numbers
name for whole numbers
is “integers.”
is “integers.”
DE
CIM
ALS
DE
CIM
ALS
The decimal method is
The decimal method is
used to display numbers
used to display numbers
other than whole
other than whole numbers, fractions, or
numbers, fractions, or percentages such as,
percentages such as, 0.80, 1.25, 1.732, and so
0.80, 1.25, 1.732, and so
on. on.
FRA
CTI
ON
SFR
AC
TIO
NS
A fraction represents part of a whole
A fraction represents part of a whole
number. If you use a calculator for
number. If you use a calculator for
adding, subtracting, multiplying, or
adding, subtracting, multiplying, or
dividing, you need to convert the
dividing, you need to convert the
fraction to a decimal or whole number.
fraction to a decimal or whole number.
To change a fraction to a decimal or
To change a fraction to a decimal or
whole number, divide the numerator
whole number, divide the numerator
(the top number) by the denominator
(the top number) by the denominator
(the bottom number).
(the bottom number). Examples Examples 1 6 = one divided by six = 0.166
⁄1 6 = one divided by six = 0.166
⁄ 2 5 = two divided by five = 0.40
⁄2 5 = two divided by five = 0.40
⁄ 3 6 = three divided by six = 0.50
⁄3 6 = three divided by six = 0.50
⁄ 5 4 = five divided by four = 1.25
⁄5 4 = five divided by four = 1.25
⁄ 7 2 = seven divided by two = 3.50
⁄7 2 = seven divided by two = 3.50
⁄
MU
LTIP
LIE
RM
ULT
IPLI
ER
When a number needs
When a number needs
to be changed by
to be changed by multiplying it by a
multiplying it by a percentage, the
percentage, the percentage is called a
percentage is called a multiplier. The first step
multiplier. The first step
is to convert the
is to convert the percentage to a decimal,
percentage to a decimal,
then multiply the
then multiply the original number by the
original number by the
decimal value.
decimal value.
MU
LTIPLIER
MU
LTIPLIER
WITH
EX
AM
PLE
WITH
EX
AM
PLE
EXAMPLEEXAMPLE
Question: An overcurrent
Question: An overcurrent
device (circuit breaker or
device (circuit breaker or
fuse) must be sized no less
fuse) must be sized no less
than 125 percent of the
than 125 percent of the
continuous load. If the load is
continuous load. If the load is
80A, the overcurrent device
80A, the overcurrent device
will have to be sized no
will have to be sized no
smaller than smaller than
. . Figure 1–
Figure 1–
22
(a) 75A (b
) 80A
(a) 75A (b
) 80A
(c) 100A
(d) 125A
(c) 100A
(d) 125A
Answer: (c) 100A
Answer: (c) 100A
Step 1: Convert 125 percent to
Step 1: Convert 125 percent to
a decimal: 1.25
a decimal: 1.25
Step 2: Multiply the value of
Step 2: Multiply the value of
the 80A load by 1.25 = 100A
the 80A load by 1.25 = 100A
SQU
ARE
RO
OT
SQU
ARE
RO
OT
Square Root
Square Root Deriving the square root of a number (√
Deriving the square root of a number (√ nn) is ) is
the opposite of squaring a number. The square
the opposite of squaring a number. The square
root of 36 is a number that, when multiplied by
root of 36 is a number that, when multiplied by
itself, gives the product 36. The √
itself, gives the product 36. The √36 36 equals six, equals six,
because six, multiplied by itself (which can be
because six, multiplied by itself (which can be
written as 62) equals the number 36.
written as 62) equals the number 36.
Because it’s difficult to do this manually, just
Because it’s difficult to do this manually, just
use the square root key of your calculator.
use the square root key of your calculator.
√ √ 33: Following your calculator’s instructions,
: Following your calculator’s instructions,
enter the number 3, then press the square root
enter the number 3, then press the square root
key = 1.732. key = 1.732. √ √ 1,0001,000: enter the number 1,000, then press the
: enter the number 1,000, then press the
square root key = 31.62.
square root key = 31.62.
If your calculator doesn’t have a square root
If your calculator doesn’t have a square root
key, don’t worry about it. For all practical
key, don’t worry about it. For all practical
purposes in using this textbook, the only
purposes in using this textbook, the only
number you need to know the square root of is
number you need to know the square root of is
3. The square root of 3 equals approximately
3. The square root of 3 equals approximately
1.732. 1.732. To add, subtract, multiply, or divide a number
To add, subtract, multiply, or divide a number
by a square root value, determine the decimal
by a square root value, determine the decimal
value and then perform the math function.
value and then perform the math function.
INTR
OD
UC
TIO
N
INTR
OD
UC
TIO
N
TO C
ALC
ULU
S
TO C
ALC
ULU
S
Introduction to Calculus
Introduction to Calculus
math\calculus.doc
math\calculus.doc 01/16/2002
01/16/2002 This brief Section seeks only
This brief Section seeks only
to provide the reader with a
to provide the reader with a
very brief and general
very brief and general concept of what calculus is
concept of what calculus is
all about.all about. The study of calculus is
The study of calculus is
customarily divided into two
customarily divided into two
parts:parts: Differential calculus
Differential calculus, and,, and,
Integral calculus
Integral calculus..
DIFFE
REN
TIAL
DIFFE
REN
TIAL
AN
D IN
TEG
RAL
AN
D IN
TEG
RAL
CA
LCU
SC
ALC
US
DIFFERENTIAL
DIFFERENTIAL
CALCULUS CALCULUS
Differential calculus is
Differential calculus is
concerned with the rate of
concerned with the rate of
changechange of one variable with
of one variable with
respect to another.
respect to another.
Differential calculus is
Differential calculus is
exemplified by the following
exemplified by the following
questions:questions:
What is the best way of
What is the best way of
describing the speed of a car
describing the speed of a car
or the cooling of a hot object?
or the cooling of a hot object?
How does the change of
How does the change of
output current of a transistor
output current of a transistor
amplifier circuit depend upon
amplifier circuit depend upon
the change of the input
the change of the input
current?current?
INTEGRALINTEGRAL
The study of
integration and
its uses, such as
in calculating
areas bounded
by curves,
volumes
bounded by
surfaces, and
solutions to
differential
equations.
EX
AM
PLE
SE
XA
MPL
ES