Theory and Calculations

Theory and Calculations
© Ted “Smitty” Smith E Light Electric Services, Inc.

The first several slides of this presentation are a review of calculations. Read them over and take some notes as they will help you on your journeyman’s exam as well as while doing this drill. Click the slide to advance to the next slide as you are ready. You will reach a slide which says “START”. This is the beginning of the timed portion of the drill. Click that slide and the questions slides will start running. Each slide will remain in place for 3-5 minutes depending on the difficulty of the calculation. A sound will go off letting you that it has moved to the next slide. Attempt to answer the question. If you finish before the timer goes off, click the slide and it will go to the next question. If you do not finish, simply stop working that problem and start on the next. When you reach the end of the timed portion you will see a slide that says “STOP”. Click on that slide and each of the questions will reappear and this time you can click them to move to the next slide, which will have the answer. Please call me if you have any issues or questions and I will be happy to arrange a time for us to review. Directions

Ohms Law One watt of power will be produced when one ampere of current is passed through one ohm of resistance if one volt of electromotive force is present. The key is to remember the two circles when applying ohms law. P=I x E E=I x R

Three Phase Relationships in Transformers
All three phase systems have two values for current and EMF. Phase and Line Line is the value measured line to line. A to B, B to C, A to C Phase is the value measured on a single coil

Three Phase Windings All three phase systems are made of three coils or windings. Each winding produces voltage and current Each winding has two leads The two leads from each single winding has to be connected together to form three wires of the three phase system. A, B and C We can wire these six wires together in series or parallel and how they are wired will change the line and values.

Relationships Series Parallel Line Voltage and Phase Voltage are Equal
Line current is times greater than phase current Parallel Line voltage is times greater than phase voltage Line current and phase current are equal

Three Phase Transformers
Turns Ratio The ratio of the primary to secondary turns or length Expressed in units. Such as 4:1 In this case the length of the primary conductor is four times longer than the length of the secondary conductor The voltage and current produced will be in line with this. If the primary is 480 volts the secondary will be 120 volts

Voltage Ratio This is used in the code book in locations such as the Tap rules in This is the ratio of the primary line voltage to the secondary phase voltage This means depending on the configuration of the three phase transformer this is not always equal to the turns ratio

The efficiency of three phase transformers is such that we consider them to be 100% for calculation purposes. This means that power in equals power out. Rated in KVA for this reason because the current will differ depending on the primary or secondary OVERCURRENT PROTECTION according to 450.3(B) Conductor sizing according to and

Click here to start the timed portion of the Drill

What is the total resistance of three resistors wired in parallel if each resistor is 15.6 ohms?

5.2 ohms

What is the voltage of a DC circuit that has three resistors wired in parallel? The resistors are valued at 15.6 ohms, .068 ohms and 19.1 ohms. The total current in the circuit is measured at 18.1 amperes.

16.04 volts

What is the total power used by a circuit that has three resistors wired in series of 10 ohms each and is operating at a voltage of 6 volts?

1.2 watts

Copyright 2005 Ted "Smitty" Smith
What is the minimum demand on the main service entrance of a single family dwelling that measures 3600 square feet and is equipped with a 14.2 kw range at 240 volts, a 3.6 kw water heater at 240 volts, a 4.6 kw air conditioning unit at 240 volts, a 1.2 kw dishwasher at 120 volts, a .95 kw garbage disposal at 120 volts, a 2.1 kw permanently installed trash compactor at 120 volts, and a 2.1 kw sump pump at 120 volts. The home is also equipped with 12 separately controlled baseboard heating units rated at 2.1 kw each at 240 volts. Copyright 2005 Ted "Smitty" Smith

A single family dwelling is 6300 square feet. It is equipped with 4 small appliance branch circuits, a 4.6 kw wall mounted over at 240v, a 6.2 kw wall mounted oven at 240 volts, a 3.2 kw cook top at 240 v, a warming drawer at 1.2 kw at 240 volts, a 4.7 kw dryer at 240 volts, a 3.9 kw deicing system at 120 volts, a 1.1 kw garbage disposal at 120 volts, a 5.9 kw air conditioning unit, 12 kw electric furnace at 240 volts, a 1.2 kw dish washer at 120 volts, a 4.9 kw water heater at 240 volts and three electric insta-hot water heaters at 2.1 kw at 120 volts. What is the fastened in place appliance load on the main service entrance of this dwelling? Copyright 2005 Ted "Smitty" Smith

17400 watt There are four or more fastened in place appliances so the demand is derated to 75 percent

What is the maximum branch circuit- short circuit protection allowed for a 208V, three phase, squirrel cage motor with the following nameplate ratings: 20 hp, 51.6 A FLC, 1.15 Service Factor, and Design B The short circuit protection will be done with an inverse time circuit breaker.

150 ampere inverse time breaker.

A three phase transformer has a turns ratio of 4:1
A three phase transformer has a turns ratio of 4:1. The transformer is wired Delta:Wye. The primary line voltage is 480 VAC. The secondary line current is 186 amperes. What is the primary line current?

80.54 A Wye= Line current is equal phase current. Phase current on secondary is 186 A. Transformer is wound 4:1. Current will decrease 4 times between secondary and primary because voltage increases 4 times between secondary and primary. Phase current on the primary windings will be 186/4= 46.5 amps Delta= Line current is times greater than phase current Line current on primary side will be 46.5 x 1.732= amps

What is the minimum sized copper USE conductor that can be used as a service entrance conductor for a dwelling equipped with the following: 4500 square feet of habitable space 14 kW 240V 1.2 kw 120V 3.6 kW water 240 V 5.2 kw 240 V 7.9 kw electric 240V The service is 240 volts single phase.

Light 8250 Cook 8800 Dryer 5200 App Motor Heat Total= 34900/240V= 145 amps Service size 150 A Table (B)(7) 1 Copper USE

A 480V three phase service is fed by four parallel runs of 250 kCMIL THHN conductors. An equally sized grounded conductor is run with each set of ungrounded conductors. The service is rated at 1000 amperes. A main bonding jumper conductor is installed between the grounded bus bar and the grounding electrode bus bar in the service. The bonding jumper is a bare copper 1/0 conductor. Is this an allowable installation? Copyright 2008 Ted "Smitty" Smith

No. Table (C)(1) Note 1 requires a minimum 2/0 AWG copper main bonding jumper in this application.

A size 18 THHN copper conductor installed in an ambient temperature of 78 degrees F has an ampacity of _________ amperes.

14 A 310.15(B)(16) and (B)(2)(a)

A PVC junction box that is permanently stamped as having a volume of 110 is installed as an underground junction box. The box has 4 PVC conduits entering the box. One conduit entering the box contains nine 10 AWG THHN conductors and one 12 AWG THHN equipment grounding conductor all of which terminate in the box. Another conduit entering contains nine 10 AWG THWN-2 conductors and one 12 AWG THHN equipment grounding conductor all of which terminate in the box. Two of the conduits entering the box contain eight 6 AWG THWN conductors and one 12 AWG equipment grounding conductors. All of the 6 AWG conductors are pulled through the box without terminating and a coil of 12 inches is left in each conductor for future maintenance. The 12 AWG equipment grounding conductors terminate in the box. No devices are present in the box. Is this an allowable installation?

No it is not. The volume of the box is 110
No it is not. The volume of the box is 110. The conductors need a volume of

What is the ampacity of a 14 RHW copper conductor installed in an ambient temperature of 108 degrees F?

16.4 A 310.15(B)(16) and (B)(2)(a)

A branch circuit has a load of 19.5 amperes. The load is expected to operate at periods of four hours or more continuously. The branch circuit conductors are installed in a raceway that contains a total of twelve current carrying conductors. The branch circuit conductors are 8 AWG THHN copper conductors and they are protected by a 60 ampere inverse time circuit breaker for overcurrent protection. Is this an allowable installation? Copyright 2005 Ted "Smitty" Smith

Yes it is allowed. The derated and adjusted load is amperes. An 8 AWG THHN has an ampacity of 55 amperes. Applying (C) requires we ensure that the original load of 17.5 x 1.25 for continuous duty is covered by an 8 AWG THHN in the 60 degree C column and it is and 240.4(B) allow the protection of the conductors to be done by the next higher standard size if all three conditions are met and this installation meets those conditions. So a 60 ampere overcurrent device is allowed. Copyright 2005 Ted "Smitty" Smith

A three phase transformer has a turns ration of 28. 75:1
A three phase transformer has a turns ration of 28.75:1. The transformer is wired Delta:Delta. The secondary line current is 1600 amperes. What is the primary line current on the transformer?

55.65 Amperes Secondary line current is 1600 wired delta so phase current is 1600/1.732= Current will decrease from secondary to primary times because voltage increases times from secondary to primary /28.75=32.13 Primary line current in a delta system will be times greater than phase current. 32.13 x 1.732=55.65 A

A fixed multioutlet wiremold assembly, that is 183 feet in length, is installed in an office building with a 120V, 20A duplex receptacle installed 12 inches from the end and every two feet thereafter. The wiremold is fed with three 20 ampere branch circuits and the duplex receptacles are divided evenly between the three branch circuits. Is this an acceptable installation? The devices are expected to by used non-simultaneously. Copyright 2005 Ted "Smitty" Smith

What is the minimum sized THHN wire that can be used to feed the following motor:
Three Phase, squirrel cage, 30 HP, 480 Volts, 33.6 amperes FLC, 1.15 marked service factor and the motor is NOT a design B, C or D.

6 AWG THHN Based on the 60 degree column of based on (C)

What is the minimum sized THHN copper conductor that can be used to feed six arc welders with the following ratings: 1. 50 A at 30 Duty Cycle 2. 60 A at 40 duty cycle at 10 duty cycle A at 10 duty cycle 5. 75 A at 50 duty cycle A at 60 duty cycle

250 KCMIL Determined by (A )and (B) Table Column 60 degrees C based on (C)

How many 15 ampere lighting circuits will be required for a single family dwelling that is 2650 square feet to meet the minimum requirements of the National Electric Code?

5 2650 x 3= 7950/120=66.25 amperes/ 15= 4.41 Total of 5 circuits

What is the demand on the main service entrance of a multifamily dwelling for 15 electric clothes dryers that are rated at 4.4 kW at 240 volts?

32250 VA 5000 x 15= 75000 75000 x .43= VA The 43% comes from Table There are four more dryers than 11. So the percentage of squeeze is 47-4=43.

What is the demand on the main service entrance of a multifamily dwelling for the lighting and receptacle loads for 20 apartments if each apartment is 1300 square feet?

55950 VA T220.42 3 x 1300 x 20= 78000 4500 x 20= 90000 = = = x .35= 40950 48000 x .25= 12000 = VA

What is the maximum sized instantaneous trip breaker that can be used to protect the following motor for short circuit protection: 50 HP, 208V, three phase, squirrel cage motor, amperes FLC, marked service factor of 1.15?

1200 Amperes Based on T and for standard sized fuses and circuit breakers.

What is the calculated load on the branch circuit of a three phase, 480V, 50 HP squirrel cage motor that operates a ore rolling chute? The motor has a nameplate rating of 61.6 amperes. The motor is rated to operate on intermittent duty and is rated for 60 minute operation.

55.4 amperes 430.22(E)

What is the minimum sized THHN conductor needed to feed a short time duty rated motor that is single phase, 208V, 5 HP, 26.9 amperes, and is rated to operate 5 minutes? The motor is rated at 75 degrees C.

10 AWG 29.59 amperes

Amperes

amperes

What is the volume allowance required for the following junction box which has a total of nine 12 AWG THHN conductors entering the junction box, one of which is an equipment grounding conductor. The box will contain one duplex receptacle, has no internal clamps, and no luminairie studs or hickeys.

A load of 23 amperes is being fed by a circuit consisting of 10 AWG THHN copper conductors. The conductors are installed in a conduit that is installed on a rooftop in the direct sunlight. The conduit is installed 12” above the roof from the bottom of the conduit. The average ambient temperature for the area in which the conduit is installed is 87 degrees F. The conduit contains a total of three current carrying conductors. Is this an acceptable installation? Copyright 2005 Ted "Smitty" Smith

Yes, it is rated to carry 32.8 amperes.

Three 10 AWG THHN, four 6 AWG THW and five 8 AWG TW conductors are installed in a one and one half inch electrical metallic tubing conduit that is 280 feet in length. Is this an acceptable installation? Copyright 2005 Ted "Smitty" Smith

What is the ampacity of 2 AWG TW aluminum conductor installed in a conduit that is installed in a boiler room with an ambient temperature of 103 degrees F and the conductor is installed in a conduit with a total of 17 current carrying conductors?

30.75 Amperes

A 4 x 1 ½ square metal box is installed with two duplex receptacles
A 4 x 1 ½ square metal box is installed with two duplex receptacles. The box has a total of three 12 AWG MC cables entering the box, each MC cable is a 12/2 with ground. The box contains no internal cable clamps, and no luminairie studs or hickeys. Is this an acceptable installation?

No, the conductors and devices require a volume allowance of 24
No, the conductors and devices require a volume allowance of and Table (A) lists a 4 x 1 ½” metal box as having a volume of 21.0

What is the minimum sized service, minimum sized aluminum grounded conductor and minimum sized copper grounding electrode conductor required for a machine shop if the shop is equipped with the following: 100 feet of multioutlet assembly not expected to be used simultaneously 75 duplex receptacles at 120V The following motors Single phase, 208V, ½ hp, 1.9 A varying duty motor, 5 mins Single phase, 208V, 5 hp, 28.7A intermittent duty motor, 30 mins Single phase, 208V, 10 hp, 48.6 A 5 minute, short time duty motor, 15 mins (6) single phase, 120V, 1 hp, 120V, 14.8 A, intermittent duty motors, 30 mins A 208V three phase, 58.7 A rated roof mounted HVAC system The machine shop is square feet with 5000 square feet classified office and square feet classified warehouse. The service will be 208V, three phase. The service entrance conductors will be THHN aluminum. All circuits are specified to be rated at 75 degrees C.

300A ampere service, 500 kcmil AL SE conductors, 500 kcmil AL grounded conductor, 2 AWG copper grounding electrode conductor Lighting= = va Recepts= VA = 7100*.5=3550 = va Motors = Single phase, 208V, ½ hp, 1.9 A varying duty motor, 5 mins va Single phase, 208V, 5 hp, 28.7A intermittent duty motor, 30 mins va Single phase, 208V, 10 hp, 48.6 A 5 minute, short time duty motor, 15 mins va (6) single phase, 120V, 1 hp, 120V, 14.8 A, intermittent duty motors, 30 mins va Roof Mounted HVAC x x 208= Total = / 208 /1.732= amperes= 300A service 300A at 75C Aluminum = 500 kcmil Service Entrance Conductors Neutral Loads Lighting= Recep= V motors= Total Neutral Load= va /120V= A Requires the neutral to be no larger than the ungrounded conductors so this would require 500 KCMIL grounded conductor T Requires a 2 AWG copper grounding electrode conductor if the service entrance conductors are 500 kcmil aluminum.

Is it allowable to add three 10 AWG THHN conductors to an existing conduit that is 150 feet in length and currently has eight 6 AWG THWN conductors and one 12 AWG THHN conductor installed? The conduit is a 1 ¼” inch electrical metallic tubing.

Yes. The total area used by the conductors once the three 10 AWG conductors are added will be inches and a 1 ¼” EMT at 40% fill has an allowance of only .598 inches.

A 39.6 ampere load is fed with a 6 AWG THW conductor that is installed in a conduit with a total of 7 current carrying conductors. The conduit is installed in a room that has an ambient temperature 38 degrees Celsius. Is this an acceptable installation?

Yes it is acceptable. The conductor is rated at 40.04 amperes.

CLICK HERE TO PROCEED WITHOUT THE TIMER AND REVIEW THE QUESTIONS AND ANSWERS

What is the total resistance of three resistors wired in parallel if each resistor is 15.6 ohms?

5.2 ohms

What is the voltage of a DC circuit that has three resistors wired in parallel? The resistors are valued at 15.6 ohms, .068 ohms and 19.1 ohms. The total current in the circuit is measured at 18.1 amperes.

16.04 volts

What is the total power used by a circuit that has three resistors wired in series of 10 ohms each and is operating at a voltage of 6 volts?

1.2 watts

What is the minimum demand on the main service entrance of a single family dwelling that measures 3600 square feet and is equipped with a 14.2 kw range at 240 volts, a 3.6 kw water heater at 240 volts, a 4.6 kw air conditioning unit at 240 volts, a 1.2 kw dishwasher at 120 volts, a .95 kw garbage disposal at 120 volts, a 2.1 kw permanently installed trash compactor at 120 volts, and a 2.1 kw sump pump at 120 volts. The home is also equipped with 12 separately controlled baseboard heating units rated at 2.1 kw each at 240 volts. Copyright 2005 Ted "Smitty" Smith