On The Job Mathematics



On The Job Mathematics

For Electrical

By Steven W. Anderson

AM or PM Class

Name:________________________

School:____________ Grade:_____

Date Started:__________ Age:____

Directions: Read each of the problems carefully and answer them in order. Refer to the pictures and Reference Guide as needed for extra help working out the problems. Do your own work and don't distract other students from their work by asking them questions. For additional help ask your teacher. Write down all scratch-work close to the problem you are working on, save it, do not erase, this will help if you need to make corrections later. All work will need to be 100% correct before you will be given credit for this math unit.

For residential and light commercial buildings we use many math skills estimating and installing the electrical system. One of the first tasks you need to do is estimate the electrical materials needed. Use the electrical plan for House A. on the last page of this unit to answer the following questions. A regular duplex receptacle (shown at right) will hold two appliances. The symbol of a duplex will look like this: on the electrical plan. How many regular duplexes are shown on the electrical plan for House A.? Note: Do not count other special duplexes like those marked with GFI or WP.

Duplexes needed for kitchen and dinning room = ________

Duplexes needed for master bedroom = ________

Duplexes needed for living room = ________

Duplexes needed for hall = ________

Duplexes needed for bedroom # 3 = ________

Duplexes needed for bedroom #2 = ________

Total regular duplexes shown on the electrical plan for House A. = ________

If each regular duplex cost $1.97 and the electrical supply center gives you a 10% discount, what will be the cost of the regular duplexes for House A.? Note: Add 6% for tax after deducting for discount.

Cost for regular duplexes needed for House A. = $________

Amount of discount = $__________

Amount of tax = $__________

Total cost for regular duplexes needed for House A. = $________

A GFI (ground fault interrupter) duplex is a special type duplex (shown at left)

that is used in areas where exposure to water or moisture is possible. A GFI symbol will look like this: on the electrical plan. How many GFI duplexes are shown on the electrical plan for House A.? Note: Some GFI duplexes will have waterproof (WP) covers.

Total GFI duplexes shown on the electrical plan for House A. = ______

If each GFI duplex cost $5.78 and the electrical supply center gives you a 10% discount, what will be the cost of the regular duplexes for House A.? Note: Add 6% for tax after deducting for discount.

Cost for GFI duplexes needed for House A. = $________

Amount of discount = $__________

Amount of tax = $__________

Total cost for GFI duplexes needed for House A. = $________

Each regular duplex and GFI duplex will be placed into an electrical box (a variety of electrical boxes shown at right).

If each electrical box cost $2.62 and you could get a 10% discount, how much would all the duplex boxes cost you for House A.? Note: Add 6% tax after you reduce for discount.

Total number of regular and GFI duplex boxes = ______

Cost for duplex boxes needed for House A. = $_______

Amount of discount = $__________

Amount of tax = $__________

Total cost for duplex boxes needed for House A. = $_______

The NEC (National Electrical Code) says you must have at least one GFI duplex on the exterior of residential homes. Each GFI duplex located outside a home needs to be placed into a waterproof (WP) type electrical box. If a WP box cost you an extra $2.03 each, what will be the total extra cost for the exterior duplex boxes needed for House A.?

Note: Remember to deduct 10% discount before adding 6% tax.

Extra cost for WP boxes for House A. duplexes = $________

Amount of discount = $_______

Amount of tax = $_______

Total extra cost for WP boxes needed for House A. = $_________

What is your total cost for all the duplexes and duplex boxes for

House A.?

Total cost for boxes and duplexes for House A. = $_________

If the labor time to wire and install a duplex or switch in an electrical box is estimated at .95 hour, how many labor hours approximately will it take to install all the duplexes for House A.?

Labor hours to wire and install all duplexes for House A. = _________

The American wire gauge (AWG) is used to measure the size of electric wires (see picture at right).

For example an AWG No. 14 wire is .064" or

(64 mills) in diameter. The larger the AWG number the smaller the diameter of wire. For example an AWG

No. 12 size wire has a larger diameter than a No. 14 wire.

According to the AWG fill in the following blanks:

Which is smaller 16 or 14? = _______

Which is larger 14 or 12? = _______

Which is larger 0 or 3? = _______

Which is smaller 8 or 10? =_______

Each wire size has a NEC maximum allowed ampacity (number of amps it can safely handle) as shown in the wire chart below. If you need to install a hot water heater that will be on a 30-amp breaker what is the minimum wire size the NEC will allow? Fill in remaining wire sizes needed.

|Wire Size |Max. Ampacity |

|No. 14 | 15 |

|No. 12 | 20 |

|No. 10 | 30 |

|No. 8 | 40 |

|No. 6 | 50 |

|No. 4 | 70 |

|No. 2 | 95 |

|No. 1/0 | 125 |

|No. 2/0 | 145 |

|No. 3/0 | 165 |

For years, in many homes,

No. 14 wire (handling a maximum of 15 amps) was commonly used for most duplexes and general lighting circuits. Many electricians today use larger No. 12 wire, which is able to handle 20 amps. The most common type of wire used for homes is nonmetallic-sheathed cable (shown at the right). It is commonly called romex and

is mostly sold in 250' rolls.

If it takes 8 rolls to wire the duplexes for the House A. and it costs $24.78 per roll, how much will the wire cost? If you get a 10% discount and sales tax is 6% what will be your final cost?

Romex cost to wire duplexes for House A. = $__________

Amount of discount = $__________

Amount of tax = $__________

Total romex cost to wire duplexes for House A. = $__________

In determining the number of lighting circuits for a home, the NEC recommends one 20-ampere circuit for every 500 Sq. Ft. of livable floor area (or 375 Sq. Ft. for one 15-amp circuit). If House A. is 1048 Sq. Ft., how many 20-amp lighting circuits should you have? How many 15-amp lighting circuits should you have?

Note: Round your answers off to the nearest whole number.

20-amp lighting circuits for House A. = _________

15-amp lighting circuits for House A. = _________

The NEC recommendations in the previous problem are the minimum lighting requirements. A better practice is supplying one 20-ampere circuit for each 400 Sq. Ft. of living space. Using this method, how many lighting circuits should be planned for House A.?

20-amp lighting circuits for House A. = _________

The NEC requires, in addition to the lighting recommendations, many other minimum required circuits for homes. Each one of these circuits is connected to a circuit breaker in a service panel like the one shown at right. How many more circuits' will House A. need, if you follow the specifications listed below?

House A. electrical specifications: The electrical system will contain three 20-amp circuits in the kitchen, one 15-amp circuit for the refrigerator, one 20-amp circuit for the microwave oven, one 20-amp circuit for the dining room, one 20-amp circuit for the GFI near the back door, one 20-amp circuit for the bath-room, two 15-amp circuits for the master bedroom, one 15-amp circuit each for bedrooms 2 and 3, one 20-amp circuit for the GFI near the front door, two 20-amp circuits for the living room, one 15-amp circuit for the unfinished basement (lighting), one 20-amp circuit for the laundry (washer and gas dryer), one 15-amp circuit for the gas furnace, one 20-amp circuit for dish-washer, one 20-amp circuit for a garbage disposal, and one 20-amp circuit for future garage addition.

Number of 15-amp circuits = ______

Number of 20-amp circuits = ______

Total number of circuits = ______

In determining the size of the service entrance (shown at right) and the service panel for a home, the code allows you to add the total watts for appliances that will be used in the house and then divide by the voltage to get the entrance service size needed. Look at the units listed in blue and determine how many total watts there will be for the type of appliances listed in chart below. Washing machine 750 watts, dishwasher 1325 watts, air-conditioner 1430 watts, 15 incandescent lamps 100 watts each, two electric blankets 175 watts each, sump pump 300 watts, three T-V units 300 watts each, stereo 325 watts, refrigerator 275 watts, water pump 300 watts, freezer 465 watts, water heater 4500 watts.

Watts of lighter units = ________

Watts of intermediate units = ________

Watts of heavier units = ________

Total watts of all units = ________

When determining the total watts used in a home the code allows for a "demand factor". Lighter and intermediate units totaling above 3000 watts will count only at a 35% rate because all these units will not be operating at the same time. For example, if you determined for lighter and intermediate units of your house there were 9000 watts, the first 3000 would count at 100% while the balance of 6000 watts would count only at 35% (see below).

If 9000 watts was your house total for lighter and intermediate units:

The first 3000 watts will be = net watts………………………………………………………. 3000

The balance left over is 6000. It will be multiplied times 35%. 6000 x 35% = net watts …. +2100

Total net watts then will be = 5100

Using the "demand factor" what will be the net watts for the house on page 6? Note: The 35% factor is only applied to the lighter and intermediate units as described on page 6. Heavier units are figured at full wattage.

Note: Round off answer to the nearest full watt.

Watts for lighter and intermediate units from page 6 = _________

The first 3000 watts will be = ……………………………………. net watts _________

The balance left over is _________x 35% = ……………………..net watts _________

The total watts for heavier units =…………………………………………… +_________

Total net watts = __________

The NEC provides minimum required watts for home lighting at 3 watts per Sq. Ft. For example the minimum lighting watts for a 1500 Sq. Ft. home is 4500 watts. What would be the minimum lighting watts for House A. with 1048 Sq. Ft.? Note: Round answers off to nearest whole number.

Minimum required lighting watts for House A. = _______

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Wire size needed for 30 amp hot water heater = No.________

Wire size needed for 50 amp electric range = No.________

Wire size needed for 40 amp Air Conditioner = No.________

Wire size needed for 20 amp Air Compressor = No.________

Wire size needed for 15 amp refrigerator = No.________

Wire size needed for 35 amp Clothes dryer = No.________

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