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Transcript of PROJECT JUGAAD
PROJECT JUGAAD
WAY
TOWRDS
SUCCESS
Mathematics
in Electricity
By: HAZADOUS GEMS4
Math
em
ati
cs in
Ele
ctro
nic
s
Mathematics in Electronics
Electrical Engineering usually include
Calculus (single and multivariable),
Complex Analysis, Differential Equations
(both ordinary and partial), Linear Algebra
and Probability. Fourier Analysis and
Z-Transforms are also subjects which are
usually included in electrical engineering
programs.Of these subjects, Calculus and
Differential equations are usually
prerequisites for the Physics courses
required in most electrical engineering
programs (mainly Mechanics,
Electromagnetism & Semiconductor
Physics). Complex Analysis has direct
applications in Circuit Analysis, while
Fourier Analysis is needed for all Signals &
Systems courses, as are Linear Algebra
and Z-Transform.
Ele
ctri
cian’s
M
ath
sIn
troduct
ion
Numbers can take different forms:
Whole numbers: 1, 20, 300, 4,000,
5,000 Decimals: 0.80, 1.25, 0.75, 1.15
Fractions: 1/2, 1/4, 5⁄8, 4⁄3
Percentages: 80%, 125%, 250%,
500% You’ll need to be able to convert
these numbers from one form to
another and back again, because all
of these number forms are part of
electrical work and electrical
calculations. You’ll also need to be able to do some
basic algebra. Many people have a
fear of algebra, but as you work
through the material here you’ll see
there’s nothing to fear.
WH
OLE
N
UM
BER
S
Whole numbers are exactly what the term
implies. These numbers don’t contain
any fractions, decimals, or percentages. Another
name for whole numbers is “integers.”
DEC
IMA
LS
The decimal method is
used to display numbers other than whole numbers, fractions, or percentages such as,
0.80, 1.25, 1.732, and
so on.
FRA
CTIO
NS
A fraction represents part of a whole
number. If you use a calculator for
adding, subtracting, multiplying, or
dividing, you need to convert the
fraction to a decimal or whole
number. To change a fraction to a
decimal or whole number, divide the
numerator (the top number) by the
denominator (the bottom number).
Examples 1⁄6 = one divided by six = 0.166
2⁄5 = two divided by five = 0.40
3⁄6 = three divided by six = 0.50
5⁄4 = five divided by four = 1.25
7⁄2 = seven divided by two = 3.50
MU
LTIP
LIC
ATIO
N
AN
D D
IVIS
ION
W
ITH
PO
WER
S
When multiplying with powers of 10, add the
exponents algebraically.
examples: (1) 106 x10-2 = 106-2 = 104
(2) 10-6 x104 = 10(-6+4) = 10-2
(3) 103 x10-9 x100 = 10+3-9+0 = 10-
6
note: 100 º 1 (multiplying
by one does not change
anything)
MU
LTIP
LIER
When a number needs
to be changed by multiplying it by a percentage, the percentage is called a
multiplier. The first step is to convert the
percentage to a decimal, then multiply
the original number by
the decimal value.
MU
LTIP
LIER
WIT
H E
XA
MPLE
EXAMPLE
Question: An overcurrent
device (circuit breaker or
fuse) must be sized no less
than 125 percent of the
continuous load. If the
load is 80A, the
overcurrent device will
have to be sized no
smaller than .
Figure 1–2
(a) 75A
(b) 80A
(c
) 100A (d)
125A
Answer: (c) 100A
Step 1: Convert 125
percent to a decimal: 1.25
Step 2: Multiply the value
of the 80A load by 1.25 =
100A
SQ
UA
RE R
OO
T
Square Root Deriving the square root of a number (√ n) is
the opposite of squaring a number. The square
root of 36 is a number that, when multiplied by
itself, gives the product 36. The √36 equals six,
because six, multiplied by itself (which can be
written as 62) equals the number 36.
Because it’s difficult to do this manually, just
use the square root key of your calculator.
√ 3: Following your calculator’s instructions,
enter the number 3, then press the square root
key = 1.732. √ 1,000: enter the number 1,000, then press
the square root key = 31.62.
If your calculator doesn’t have a square root
key, don’t worry about it. For all practical
purposes in using this textbook, the only
number you need to know the square root of is
3. The square root of 3 equals approximately
1.732. To add, subtract, multiply, or divide a number
by a square root value, determine the decimal
value and then perform the math function.
Consider that both the bulbs are giving out equal-level of brightness. So, They're losing the same amount of heat (regardless the fact of AC or DC). In order to relate both, we have nothing to use better than the RMS value. The direct voltage for the bulb is 115 V while the alternating voltage is 170 V. Both give the same power output. Hence, V rms =V dc =V ac 2 √ =115 V (But Guys, Actual RMS is 120 V). As I can't find a good image, I used the same approximating 120 to 115 V.
EXAMPLES
INTR
OD
UC
TIO
N
TO
CA
LCU
LUS
Introduction to Calculus
math\calculus.doc 01/16/2002 This brief Section seeks only
to provide the reader with a
very brief and general
concept of what calculus is
all about. The study of calculus is
customarily divided into two
parts: Differential calculus, and,
Integral calculus.
DIFFE
REN
TIA
L
AN
D IN
TEG
RA
L
CA
LCU
SDIFFERENTIAL
CALCULUS
Differential calculus is
concerned with the rate
of change of one
variable with respect to
another.
Differential calculus is
exemplified by the
following questions:
What is the best way of
describing the speed of
a car or the cooling of a
hot object?
How does the change of
output current of a
transistor amplifier
circuit depend upon the
change of the input
current?
INTEGRAL
The study of
integration and
its uses, such
as in
calculating
areas bounded
by curves,
volumes
bounded by
surfaces, and
solutions to
differential
equations.