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

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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

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AN

D IN

TEG

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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.