INTRODUCTION...xiii Author s Comments...xiii Exam Preparation...xiii Difficult Concepts...xiv Textbook Errors and Corrections...xv Internet...

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1 INTRODUCTION...xiii Author s Comments...xiii Exam Preparation...xiii Difficult Concepts...xiv Textbook Errors and Corrections...xv Internet...xv UNIT 1 ELECTRICIAN S MATH AND BASIC ELECTRICAL FORMULAS...1 PART A ELECTRICIAN S MATH Whole Numbers Decimals Fractions Percentages Multiplier Percent Increase Reciprocals Squaring a Number Parentheses Square Root Volume Kilo Rounding Off Testing Your Answer for Reasonableness...6 PART B BASIC ELECTRICAL FORMULAS Electrical Circuit Power Source Conductance Circuit Resistance Ohm s Law Ohm s Law and Alternating Current Ohm s Law Formula Circle PIE Formula Circle Formula Wheel Using the Formula Wheel Power Losses of Conductors Cost of Power Power Changes with the Square of the Voltage v

2 Electrical Formulas with Sample Calculations UNIT 2 ELECTRICAL CIRCUITS...15 PART A SERIES CIRCUITS...15 Introduction Practical Uses of the Series Circuit Understanding Series Calculations Series Circuit Calculations Power Calculations Variations Series Circuit Notes Series-Connected Power Supplies...19 PART B PARALLEL CIRCUITS...19 Introduction Practical Uses of the Parallel Circuit Understanding Parallel Calculations Circuit Resistance Parallel Circuit Notes Parallel-Connected Power Supplies...22 PART C SERIES-PARALLEL CIRCUITS...22 Introduction Review of Series and Parallel Circuits Working With Series-Parallel Circuits Voltage...26 PART D MULTIWIRE BRANCH CIRCUITS...26 Introduction Neutral Conductor Grounded Conductor Current Flow on the Grounded (Neutral) Conductor Balanced Systems Unbalanced Current Multiwire Branch Circuits Dangers of Multiwire Branch Circuits NEC Requirements...31 UNIT 3 UNDERSTANDING ALTERNATING CURRENT...33 PART A UNDERSTANDING ALTERNATING CURRENT...33 Introduction Current Flow Why Alternating Current is Used How Alternating Current is Produced AC Generator Waveform...35 vi

3 Table of Contents 3.6 Sine Wave Frequency Phase Degrees Lead or Lag Values of Alternating Current...37 PART B CAPACITANCE...39 Introduction Charged Capacitor Electrical Field Discharging a Capacitor Determining Capacitance Uses of Capacitors Phase Relationship...41 PART C INDUCTION...41 Introduction Self-Induction Induced Voltage and Applied Current Conductor AC Resistance Impedance Conductor Shape Magnetic Cores Self-Induced and Applied Voltage Current Flow Phase Relationship Uses of Induction...46 PART D POWER FACTOR...47 Introduction Apparent Power (Volt-Amperes) True Power (Watts) Power Factor Unity Power Factor Power Factor Formulas Cost of True Power Effects of Low Power Factor...52 PART E EFFICIENCY...52 Introduction Efficiency Formulas...52 UNIT 4 MOTORS AND TRANSFORMERS...55 PART A MOTORS...55 Introduction Motor Principles Dual-Voltage AC Motors...55 vii

4 viii Electrical Formulas with Sample Calculations 4.3 Motor Horsepower Rating Motor Current Ratings Calculating Motor FLA Motor-Starting Current Motor-Running Current Motor Locked-Rotor Current (LRC) Motor Overload Protection Direct-Current Motor Principles Direct-Current Motor Types Reversing the Rotation of a DC Motor AC Induction Motor Alternating-Current Motor Types Reversing the Rotation of an AC Motor...65 PART B TRANSFORMERS...65 Introduction Transformer Basics Secondary Induced Voltage Transformer Turns Ratio Autotransformers Power Losses Harmonic Current Efficiency Transformer kva Rating Current Rating...72 UNIT 5 RACEWAY AND BOX CALCULATIONS...75 PART A RACEWAY FILL Understanding the NEC, Chapter 9 Tables Raceway and Nipple Calculations Existing Raceway Calculations Tips for Raceway Calculations...81 PART B OUTLET BOX FILL CALCULATIONS Sizing Box Conductors All the Same Size Conductor Equivalents Sizing Box Different Size Conductors...88 PART C PULL BOXES, JUNCTION BOXES, AND CONDUIT BODIES Pull and Junction Box Size Calculations Depth of Box and Conduit Body Sizing Junction and Pull Box Sizing Tips Pull Box Examples...94

5 Table of Contents UNIT 6 CONDUCTOR SIZING AND PROTECTION CALCULATIONS...95 PART A GENERAL CONDUCTOR REQUIREMENTS Conductor Insulation Property Allowable Conductor Ampacity Conductor Sizing Terminal Ratings Conductors in Parallel Conductor Size Voltage Drop Overcurrent Protection Overcurrent Protection of Conductors General Requirements Overcurrent Protection of Conductors Specific Requirements Equipment Conductor Size and Protection Examples PART B CONDUCTOR AMPACITY CALCULATIONS Conductor Ampacity Ambient Temperature Ampacity Correction Factor Conductor Bundling Ampacity Adjustment Factor Ambient Temperature Correction and Conductor Bundling Adjustment Factors Current-Carrying Conductors Conductor Sizing Summary UNIT 7 MOTOR CALCULATIONS Single Motor Conductors Motor Overcurrent Protection Overload Protection Branch-Circuit Short-Circuit Ground-Fault Protection Feeder Conductor Size Feeder Protection Highest Rated Motor Motor Calculations Steps Motor Calculation Review Motor VA Calculations UNIT 8 VOLTAGE-DROP CALCULATIONS PART A CONDUCTOR RESISTANCE CALCULATIONS Conductor Resistance Conductor Resistance Direct-Current Circuits ix

6 x Electrical Formulas with Sample Calculations 8.3 Conductor Impedance Alternating-Current Circuits Alternating-Current Impedance as Compared to Direct-Current Resistance Impedance PART B VOLTAGE-DROP CALCULATIONS Voltage-Drop Considerations NEC Voltage-Drop Recommendations Determining Circuit Conductors Voltage Drop Sizing Conductors to Prevent Excessive Voltage Drop Limiting Conductor Length to Minimize Voltage Drop Limiting Current to Limit Voltage Drop Extending Circuits UNIT 9 DWELLING UNIT CALCULATIONS PART A GENERAL REQUIREMENTS General Requirements Voltages Fraction of an Ampere Small-Appliance Circuits Cooking Equipment Branch Circuit Laundry Receptacle(s) Circuit Lighting and Receptacles PART B STANDARD METHOD FEEDER/SERVICE LOAD CALCULATIONS Dwelling Unit Feeder/Service Load Calculations Dwelling Unit Feeder/Service Calculations Examples PART C OPTIONAL METHOD FEEDER/SERVICE LOAD CALCULATIONS Dwelling Unit Optional Feeder/Service Calculations Dwelling Unit Optional Calculation Example Neutral Calculations General UNIT 10 MULTIFAMILY DWELLING CALCULATIONS Multifamily Dwelling Unit Calculations General

7 Table of Contents PART A STANDARD METHOD-FEEDER/SERVICE LOAD CALCULATIONS Multifamily Dwelling Unit Calculations Standard Method PART B OPTIONAL METHOD-FEEDER/SERVICE LOAD CALCULATIONS Multifamily Dwelling Unit Calculations Optional Method Multifamily Optional Method Example UNIT 11 COMMERCIAL CALCULATIONS PART A GENERAL General Requirements Conductor Ampacity Voltages Rounding an Ampere Air-Conditioning Branch Circuit Dryers Electric Heat Kitchen Equipment Laundry Equipment Lighting Demand Factors Lighting Without Demand Factors Lighting-Miscellaneous Multioutlet Receptacle Assembly Receptacle VA Load Banks and Offices General Lighting and Receptacles Signs PART B STANDARD METHOD FEEDER/SERVICE LOAD CALCULATIONS Feeder/Service Load Calculation Neutral Calculations PART C EXAMPLES Bank (120/240V, Single-Phase) Marina Mobile/Manufactured Home Park Office Building (277/480V, Three-Phase) Recreational Vehicle Park Restaurant Standard Load Calculation (120/208V, Three-Phase) PART D OPTIONAL METHOD FEEDER/SERVICE LOAD CALCULATIONS xi

8 Electrical Formulas with Sample Calculations New Restaurant Optional Method School Optional Method PART E ELECTRIC WELDERS Arc Welders Resistance Welders UNIT 12 DELTA/DELTA AND DELTA/WYE TRANSFORMERS Definitions Current Flow PART A DELTA/DELTA TRANSFORMERS Delta Transformer Voltage Delta High-Leg Delta Line Currents Delta Phase Currents Delta Phase versus Line Current Delta Current Triangle Delta Transformer Balancing Delta Transformer Sizing Delta Panel Balancing Delta Panelboard and Conductor Sizing Delta Neutral Current Delta Maximum Unbalanced Load PART B DELTA/WYE TRANSFORMERS Wye Transformer Voltage Wye Voltage Triangle Wye Transformer Current Wye Line Current Wye Phase Current Wye Transformer Balancing Wye Transformer Sizing Wye Panel Balancing Wye Panelboard and Conductor Sizing Wye Neutral Current Wye Maximum Unbalanced Load Delta versus Wye COMMERCIAL WIRE AND RACEWAY CHART FORMULAS xii