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PROJECT JUGAAD

PROJECT JUGAAD. WAY TOWRDS SUCCESS. Mathematics in Electricity. By: HAZADOUS GEMS4. Mathematics in Electronics

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PROJECT JUGAAD

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  1. PROJECT JUGAAD WAY TOWRDS SUCCESS

  2. Mathematics in Electricity By: HAZADOUS GEMS4

  3. 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. Mathematics in Electronics

  4. 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. Electrician’s MathsIntroduction

  5. 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.” WHOLE NUMBERS

  6. 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. DECIMALS

  7. 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 FRACTIONS

  8. 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) MULTIPLICATION AND DIVISION WITH POWERS

  9. 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. MULTIPLIER

  10. 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 MULTIPLIER WITH EXAMPLE

  11. 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. SQUARE ROOT

  12. EXAMPLES 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.

  13. 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. INTRODUCTION TO CALCULUS

  14. 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. DIFFERENTIAL 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? DIFFERENTIAL AND INTEGRAL CALCUS

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