UNIT 1 ELECTRICIAN S MATH AND BASIC ELECTRICAL FORMULAS...1 Introduction...1. UNIT 2 ELECTRICAL CIRCUITS...49 Introduction...49

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1 UNIT 1 ELECTRICIAN S MATH AND BASIC ELECTRICAL FORMULAS...1 Introduction...1 PART A ELECTRICIAN S MATH...1 Introduction Whole Numbers Decimal Fractions Percentages Multiplier Percent Increase Reciprocals Squaring a Number Square Root Volume Kilo Rounding Off Parentheses Testing Your Answer for Reasonableness...6 PART B BASIC ELECTRICAL FORMULAS...7 Introduction 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...14 PART C BASIC ELECTRIC METERS...16 Introduction Voltmeter DC Voltmeter DC Ammeter Clamp-on AC Ammeter Ohmmeters Wheatstone Bridge Megohmmeter...18 Conclusion...19 UNIT 2 ELECTRICAL CIRCUITS...49 Introduction...49 PART A SERIES CIRCUITS...49 Introduction Practical Uses of the Series Circuit Understanding Series Calculations Series Circuit Calculations Power Calculations Variations Series Circuit Notes Series-Connected Power Supplies...54 PART B PARALLEL CIRCUITS...54 Introduction Practical Uses of the Parallel Circuit Understanding Parallel Calculations Circuit Resistance Parallel Circuit Notes Parallel-Connected Power Supplies...59 PART C SERIES-PARALLEL CIRCUITS...59 Introduction Review of Series and Parallel Circuits Working Series-Parallel Circuits Voltage...61 PART D MULTIWIRE BRANCH CIRCUITS...62 Introduction Neutral Conductor Grounded Conductor...62 vi

2 Electrical NEC Exam Preparation Table of Contents 2.18 Current Flow on the Grounded Neutral Conductor Balanced Systems Unbalanced Current Multiwire Branch Circuit Dangers of Multiwire Circuits NEC Requirements...67 Conclusion...68 UNIT 3 UNDERSTANDING ALTERNATING CURRENT...97 Introduction...97 PART A UNDERSTANDING ALTERNATING CURRENT...97 Introduction Current Flow Why Alternating Current is Used How Alternating Current is Produced AC Generator Waveform Sine Wave Nonsymmetrical Waveform Frequency Phase Degrees Lead or Lag Values of Alternating Current PART B CAPACITANCE Introduction Charged Capacitor Electrical Field Discharging a Capacitor Determining Capacitance Uses of Capacitors Phase Relationship PART C INDUCTION 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 PART D POWER FACTOR Introduction Apparent Power (Volt-Amperes) True Power (Watts) Power Factor Unity Power Factor Power Factor Formulas Cost of True Power Effects of Power Factor PART E EFFICIENCY Introduction Efficiency Formulas Conclusion UNIT 4 MOTORS AND TRANSFORMERS Introduction PART A MOTORS Introduction Motor Principles Dual-Voltage AC Motors 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 PART B TRANSFORMERS Introduction Transformer Basics Secondary Induced Voltage Autotransformers Power Losses Harmonic Current Efficiency Transformer Turns Ratio Transformer kva Rating Current Flow Current Rating Conclusion vii

3 Table of Contents UNIT 5 RACEWAY AND BOX CALCULATIONS Introduction PART A RACEWAY FILL Understanding the NEC, Chapter 9 Tables Raceway and Nipple Calculations Existing Raceway Calculations Tips for Raceway Calculations PART B OUTLET BOX FILL CALCULATIONS [314.16] Sizing Box Conductors All the Same Size [Table (A)] Conductor Equivalents [314.16(B)] Sizing Box Different Size Conductors [314.16(B)] PART C PULL BOXES, JUNCTION BOXES, AND CONDUIT BODIES Pull and Junction Box Size Calculations Depth of Box and Conduit Body Sizing [314.28(A)(2) Ex] Junction and Pull Box Sizing Tips Pull Box Examples Conclusion Electrical NEC Exam Preparation 6.13 Conductor Bundling Ampacity Adjustment Factor [Table (B)(2)(a)] Ambient Temperature Correction and Conductor Bundling Adjustment Factors Current-Carrying Conductors Conductor Sizing Summary Conclusion UNIT 7 MOTOR CALCULATIONS Introduction Single Motor Conductors [430.22(A)] Motor Overcurrent Protection Overload Protection [430.6(2) and (A)] Branch-Circuit Short-Circuit Ground-Fault Protection [430.51] Feeder Conductor Size [430.24] Feeder Protection [430.61] Highest-Rated Motor [430.17] Motor Calculations Steps Motor Calculation Review Motor VA Calculations Conclusion UNIT 6 CONDUCTOR SIZING AND PROTECTION CALCULATIONS Introduction PART A GENERAL CONDUCTOR REQUIREMENTS Conductor Insulation Property [Table ] Allowable Conductor Ampacity [310.15] Conductor Sizing [110.6] Terminal Ratings [110.14(C)] Conductors in Parallel [310.4] Conductor Size Voltage Drop [210.19(A)(1) FPN No. 4 and 215.2(A) FPN No. 2] Overcurrent Protection [Article 240] Overcurrent Protection of Conductors General Requirements [240.4] Overcurrent Protection of Conductors Specific Requirements Equipment Conductor Size and Protection Examples PART B CONDUCTOR AMPACITY CALCULATIONS Conductor Ampacity [310.10] Ambient Temperature Ampacity Correction Factor [Table ] UNIT 8 VOLTAGE-DROP CALCULATIONS Introduction PART A CONDUCTOR RESISTANCE CALCULATIONS Conductor Resistance Conductor Resistance Direct-Current Circuits [Chapter 9, Table 8] Conductor Impedance Alternating-Current Circuits Alternating-Current Impedance as Compared to Direct-Current Resistance Impedance [Chapter 9, Table 9] 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 Conclusion viii

4 Electrical NEC Exam Preparation Table of Contents UNIT 9 DWELLING UNIT CALCULATIONS Introduction PART A GENERAL REQUIREMENTS General Requirements Voltages [220.5(A)] Fraction of an Ampere [220.5(B)] Small-Appliance Circuits [210.11(C)(1)] Cooking Equipment Branch Circuit [Table , Note 4] Laundry Receptacle(s) Circuit [210.11(C)(2)] Lighting and Receptacles PART B STANDARD METHOD FEEDER/SERVICE LOAD CALCULATIONS Dwelling Unit Feeder/Service Load Calculations (Article 220, Part III) Dwelling Unit Feeder/Service Calculations Examples PART C OPTIONAL METHOD FEEDER/SERVICE LOAD CALCULATIONS Dwelling Unit Optional Feeder/Service Calculations [220.82] Dwelling Unit Optional Calculation Examples Neutral Calculations General [220.61] Conclusion UNIT 10 MULTIFAMILY DWELLING CALCULATIONS Introduction Multifamily Dwelling Unit Calculations General PART A STANDARD METHOD FEEDER/SERVICE LOAD CALCULATIONS Multifamily Dwelling Unit Calculation Examples Standard Method Multifamily Dwelling Unit Calculations Standard Method PART B OPTIONAL METHOD FEEDER/SERVICE LOAD CALCULATIONS Multifamily Dwelling Unit Calculations [220.84] Optional Method Multifamily Optional Method Example 1 [220.84] Multifamily Optional Method Example 2 [220.84] Conclusion UNIT 11 COMMERCIAL CALCULATIONS Introduction PART A GENERAL General Requirements Conductor Ampacity [Article 100] Conductor Overcurrent Protection [240.4] Voltages [220.5(A)] Rounding an Ampere [220.5(B)] Air-Conditioning Branch Circuit Dryers Electric Heat Kitchen Equipment Laundry Equipment Lighting Demand Factors [Tables and ] Lighting Without Demand Factors [215.2(A)(1), (A)(1), and Table ] Lighting-Miscellaneous Multioutlet Receptacle Assembly [220.14(H)] Receptacle VA Load Banks and Offices General Lighting and Receptacles [220.14(K)] Signs [220.14(F) and 600.5] PART B STANDARD METHOD FEEDER/SERVICE LOAD CALCULATIONS Feeder/Service Load Calculation Neutral Calculations [220.61] PART C EXAMPLES Bank (120/240V, single-phase) Marina [555.12] Mobile/Manufactured Home Park [550.31] Office Building (277/480V, Three-phase) Recreational Vehicle Park [551.73] Restaurant Standard Load Calculation (120/208V, Three-phase) PART D OPTIONAL METHOD FEEDER/SERVICE LOAD CALCULATIONS New Restaurant Optional Method [220.88] School Optional Method [220.86] PART E ELECTRIC WELDERS Arc Welders Resistance Welders Light Industrial Calculation Conclusion ix

5 Table of Contents UNIT 12 DELTA/DELTA AND DELTA/WYE TRANSFORMERS Introduction 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 Delta/Delta Example Electrical NEC Exam Preparation PART B DELTA/WYE TRANSFORMERS Wye Transformer Voltage Wye Voltage Triangle Wye Transformers Current Wye Line Current Wye Phase Current Wye Phase versus Line Current Wye Transformer Balancing Wye Transformer Sizing Wye Panel Balancing Wye Panelboard and Conductor Sizing Wye Neutral Current Wye Maximum Unbalanced Load Delta/Wye Example Delta versus Wye Conclusion INDEX x

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