Math for Electronics
Math is very important in the electrical engineering field. The foundation of this field is math. The following is a list of revenant math related topic.
- Scientific Notation
- Engineering/Metric Notation
- Reading Resistor Codes
- Reading Capacitor Codes
Scientific Notation
This notation was created to make writing very large and very small numbers easier. For example writing a number like 0.0000000000345 can be tedious. With scientific notation this number becomes 3.45X10^-ll, which takes less time to write. Scientific notation works by using powers of 10 with an exponent referring to the number of zeros that follow the 1. Therefore:
- 10^0 = 1
- 10^1 = 10
- 10^2 = 100
- 10^3 = 1000
With negative exponents, the exponent refers to the number of zeros that are in the denominator within a fraction with 1 in the numerator. Therefore:
- 10^-0 = 1/1= 1 (Technically 0 can not be negative or positive)
- 10^-1 = 1/10
- 10^-2 = 1/100
- 10^-3 = 1/1000
Using the example above, 3.45X10^-ll would represent 3.45 X 1/100000000000 which equals 0.0000000000345. Note: Scientific notation always has one digit before the decimal place. Also, when the decimal place is moved to the left the exponent will be positive and when moving it to the right the exponent will be negative.
See if you can convert the following numbers to scientific notation:
- 658000
- 0.000476
- 5.84X10^12
- 0.000361X10^-3
Scientific Notation Calculator
Engineering/Metric Notation
This notation is similar to scientific notation. The difference is that in engineering notation the powers of 10 have exponents that are in multiplies of 3. This is so that metric prefixes can be used to make the writing of very small or very large numbers even quicker and shorter. The following table lists the powers of 10 and the prefixes and symbols associated with the powers of 10.
Using the same example used above the engineering notation that represents that number is 34.5X10^-12. (Notice that is does not matter that there is more than one number before the decimal. The rule is that there cannot be more than 3 before or less than one. The only exception applies to capacitors, explained below.) Now that we have the engineering form 34.5X10^-12, the chart above can be used to find the metric symbol need. We know that 10^-12 equals pico with the symbol p. So, now 34.5X10^-12 can be written as 34.5p. See who much shorter that is to write.
See if you can convert the following numbers to engineering notation using metric symbols:
- 6840
- 0.084200
- 3.86X10^10
- 4.23X10^-5
Reading Resistor Codes
Resistors are devices that limit the current within a circuit. To determine the amounts of resistance a circuit has you need to know how to determine the values of the resistors. The resistors are usually marked with colored bands which are wrapped around them. Each color represents a number or a percentage. With a four band resistor, the first two bands are values, the third band is the multiplier and the fourth band is the tolerance. The following shows the values of each color.
- Black = 0
- Brown =1
- Red = 2
- Orange = 3
- Yellow = 4
- Green = 5
- Blue = 6
- Violet = 7
- Gray = 8
- White = 9
- Gold = +/- 5%
- Silver = +/-10%
- None (no forth band) = +/-20%
Example: If the four band resistor’s color-code is: 1st band = red, 2nd band = brown, 3rd band= black, and the 4th band = silver; than value of the resistor is 21 ohms +/-10%. Red = 2, brown = 1, the number of zeros is none which is represented by the multiplier of black = 0, and the tolerance is silver = +/-10%.
See if you can convert the following resistor color-codes into resistor values, they are in chronological order.
- brown, red, blue, none
- gray, violet, red, gold
- white, green, black, none
- yellow, orange, yellow, silver
Resistor Color Code Calculator
Reading Capacitor Codes
Capacitor codes are somewhat similar to the resistor code, but most do not use color (just numbers and letters). Therefore, the first two numbers are values, the third is the multiplier, and the tolerance is expressed with a letter. (Note: the code it is represents the capacitor value in the pico farads, unless specified different.) Example: If a capacitor has the code 104 its value would be 100,000 pF, which can also be a express in microfarads (as 0.1uF). Capacitors with a letter symbol after the number code have a tolerance that is represented by the letter. The most common tolerance letters used are J = +/-5% and K= +/-10%. Example: 104K would have the tolerance of +/-10%.
See if you can convert the following capacitor codes into capacitor values.
- 103J
- 281K
- 615J
- 940K
Capacitor Code Calculator
Answers to all the problems above.
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