Guidelines for Calculations Units with Prefixes and Significant Figures

Objectives of this lecture Introduce the electrical quantities or variables that are used in the field of Electrical and Computer Engineering. Present the prefixes to the units associated with the variables that will be used frequently in this course. Review significant figures. Explain how you should present the results of your calculations in this course.

Quantity or Variable Name Basic Measure Symbol Unit Time Second t s Temperature Kelvin (Celsius) T K (oC) Resistance Ohm R W Capacitance Farad C F Inductance Henry L H Charge Coulomb Q or q Electric Current Ampere (Amp) I or i A Voltage Volt V or v V Power Watts P or p Energy Kilowatt-hours w kW-hr Frequency or Cycles per second Hertz f Hz Angular Frequency radians/s Units

Uppercase or Lowercase Symbols Using an uppercase symbol means that either the value of the variable is a constant or the value is the average of a time-varying signal. Using a lowercase symbol means that the value of the variable is what the value was at the instant that you measured or calculated the value.

Prefixes Exponent Name Prefix 1018 Exa E 10-1 Deci d 1015 Peta P 10-2 Centi c 1012 Tera T 10-3 Milli m 109 Giga G 10-6 micro 106 Mega M 10-9 nano n 103 Kilo k 10-12 pico p 102 Hecto h 10-15 femto f 101 Deka da 10-18 atto a 100 N/A none

Significant Figures Give a reader an indication of how confident you are in the accuracy of the answer that you are presenting. Electrical and electronic components are commonly binned into what is known as nominal values. The range of values within each bin is known as the component tolerance. For example, a 2 kW resistor with a 5% tolerance could actually have a resistance value between 1.90 – 2.10 kW.

Expected Format Determine whether the variable name should be written upper or lower case. Use the proper unit for the variable. Write your answer in scientific notation where all numbers include a factor of ten raised to an exponent – even if the exponent is zero. Round the value of the digit in the one-hundredths place up if the digit in the one-thousandths place is equal to or greater than 5. Rewrite the number such that the exponent is equal to closest multiple of 3. Replace the factor of ten raised to an exponent with the appropriate prefix.

Example 1 Suppose you calculated that the average power generated by a solar cell array is 21,372 Watts. If you wrote this value as your final answer to a question, you will lose some points. Follow the steps outlined in the previous slide.

Example 2 Suppose you measure the instantaneous current flowing from the battery in your Tablet PC to power the screen and the rest of the electronics and determine that it is -0.12849 amperes.

Exceptions We use scientific notation when writing the values for Coulombs and occasionally for energy, frequency, and angular frequency. Other variables where the answers are written using scientific notation include resistivity and conductivity.

Summary Examples of how your answers should be written using appropriate symbols, significant figures, and units with prefixes. I will indicate when your answers should be written in scientific notation for the cases where this format is used.