| Circuit Challenges
| Lesson Idea by:
Dave Ward, Rutland Senior Secondary School
Central Okanagan School District
Most of what electrical engineers do has some math
involved, says Jim Clousten, the senior engineer for the Southern
Interior region of B.C. Hydro.
"I use math for power calculations, figuring out
the load on circuits, and determining several factors involved in a
power system," he says. The simplest calculations may be completed with
a calculator, while computer programs are used in more complex
Clousten also uses math to calculate "fault
levels." In a house, the fault level is the level at which a breaker
"blows." (A breaker "blows" when it automatically turns off because of
a circuit problem.)
Another item used to control the possible
excessive flow of electricity is a fuse. A fuse is connected directly
into an electrical circuit. If the current surges to a dangerous level,
the thin metal wire in the fuse melts. This breaks the circuit, thereby
preventing the wires from overheating, which may cause a fire. For
safety reasons, a breaker or fuse of greater capacity than that
specified for a particular circuit should never be used.
The prospect of electrical surges and fire must
also be considered in commercial and industrial settings, especially
when large amounts of electrical energy are being supplied to customers.
In pairs, list the electrical "plug-in" appliances
and devices that are commonly found in a home. Note whether you think
they would be heavy, medium or low-power devices. Next, compare your
list with the attached results from a survey of home electrical
equipment. Any particular observations?
Answer the following questions:
- How do you check the power and current ratings
of an electrical device?
- How many outlets and/or lights may be joined as
part of one circuit?
- How are houses equipped to monitor the safety
level of circuits?
- How much power is commonly available for basic
Exchange your answers with another pair in the
class. Any questions? You may like to invite an electrical engineer, or
an electrical expert from the city hall inspection department, to visit
Principles Section A:
In any electrical work, you must be concerned with
the safety of the circuit. Therefore, the amount of power in the
circuit has to be balanced with the current and other particulars of
the wiring system.
Imagine that you're the person in charge of
determining the amount of power required for a small housing
development to be built in your area. The power will be supplied from a
special source called a transformer. The transformer will be situated
on a tall power pole, or in a well-protected box to be mounted on a
ground-level concrete pad.
The subdivision has 13 lots. Ten properties are to
receive 200 amp/120 volt service, and three will receive 400 amp/120
volt service. The latter properties require a different level of
service because of equipment that's going to be used in those homes.
The transformer is a
special piece of equipment that controls the ratio of current to
voltage in an electrical system. Its size must be determined for the
supply of electricity to the subdivision.
To calculate the amount of
basic load that the transformer is required to provide for the small
housing development, use the following formula:
watts = amps
W = A x V
Therefore, if there are 10
properties with 200 amp/120 volt services, then the total power needed
200 x 120 x 10 =
To convert large numbers of
watts into more manageable terms, divide by 1,000. This creates a
measure of kilowatts, with the symbol kW.
240,000 W / 1,000
= 240 kW
Now, calculate the amount
of power needed to supply the three houses using 400 amp/120 volt
service. Convert your answer to kilowatts.
What is the total power
required for all 13 houses in the subdivision?
Check your answers against
the solution for Principles Section A below.
Principles Section B:
While houses and small
businesses normally utilize standard "single-phase" electricity,
electrical power companies (or utility companies as they are often
called), may supply power to transformers through what is called
"three-phase" lines. (These different electrical systems can be studied
in more depth during your science courses.)
The power in a three-phase
system is measured in volt-amps. The formula used to evaluate such
Sq. root of 3 x voltage (volts) x current (amperes)
Any fuse that is put in the
electrical system to prevent problems, even in a transformer, must be
able to handle the amps flowing from the transformer at full load.
A large shopping mall is
being built in your community. The developers have decided to install
their own 1,000,000 volt-amp transformer to supply the mall's power.
Your utility company will provide 25,000 volts from your service lines
to the mall's transformer. You have a choice of using one of three
fuses: 20, 23 or 25 amp. Which one should you use?
Check your answer against
the solution for Principles Section B below.
Rob Maschek of West Kootenay Power says the
company supplies electricity to the following businesses, each having
its own transformer.
- 775,000 volt-amps -- for a wholesale warehouse
- 2.5 million volt-amps -- for a super-sized
- 4.0 million volt-amps -- for a truck
If the power supplied from the service lines is
rated at 12,470 volts, what size fuse should each business use to
protect itself from receiving too much current? Use the power
(volt-amp) formula to calculate the solutions.
Check your answers against the solution for Learn
Determine the current (amps) or watt values for
each of the appliances listed in the survey of home electrical
equipment. Take note of the electrical service provided for the house
at the top of the page. Use the formula: watts = volts x amps.
How many of the appliances or devices have less
than a 15 amp current rating? Which ones have a 30 amp, 40 amp, or even
larger amperage rating? Is it possible to have several devices on the
same circuit, as long as the 15 amp capacity of a breaker is not
reached? What would happen if you did overstep a 15 amp level of
You have eight strings of Christmas lights, each
with 25 bulbs of 7 watt rating. If you put them together on one circuit
in your house, which has a 120 volt service, will you "blow" a 15 amp
breaker when they are turned on?
If the same Christmas lights are left on for five
hours each night for 20 days, at a cost of 5.97 cents per kilowatt/hour
(kW-h), how much will your power bill increase in the month of December?
How much will it cost per year to operate an
electric clock with a 6 watt rating, at a cost of 5.177 cents per kW-h?
- For a fun project, using square grid paper and
an appropriate scale, try to design one of the following for homework!
- a small subdivision
- a small commercial center
- a medium-sized industrial area
- any other useful development for your
community that would use electricity on a consistent basis
After a visit by an electrical expert, a field
trip to an appropriate electrical supply station, or maybe even a visit
to the electrical center for your school, and after researching the
three-phase voltage provided in your area; calculate the amount of
power required to service your development.
What size of fuses or breakers (relative to
current), are required for your proposed design?
- Discuss: North Americans tend to use more
energy per person than people in most other countries. How could we be
more energy efficient, particularly in our homes?
- Discuss: Given the unfortunate electric power
problems in parts of the North East in January 1998, discuss with your
class some possible concerns power companies may have in terms of
changing the way electricity is supplied to customers.
Electrical Equipment in a Home
200 amp/120 volt service
General Equipment Watts. Amps.
Refrigerator _____ 9.5
Washer _____ 9.0
Dishwasher _____ 9.5
Microwave oven _____ 12.0
Clothes dryer _____ 25.0
Hot Water tank 6,000 _____
Range/Oven 13,100 _____
Furnace _____ 112.0
Soldering iron _____ 1.2
Hand drill _____ 2.1
Small freezer _____ 2.6
Jig saw _____ 3.0
Circular saw _____ 11.0
5 x 100 W bulbs _____ _____
Can opener _____ 1.5
Mixer 400 _____
Toaster 800 _____
Coffee maker 1200 _____
Popcorn maker 1240 _____
Bathrooms: (2 1/2)
8 x 60 W bulbs _____ _____
6 x 60 W bulbs _____ _____
3 fans at 1.2 amps _____ _____
Hair dryer 1400 _____
Ceiling lights 18x75 W _____ _____
Track lights 6x75 W _____ _____
Fluorescent 3x93 W _____ _____
Table lamps 4x150 W _____ _____
Desk lamps 2x60 W _____ _____
2x60 W _____ _____
1x150 W _____ _____
5x100 W _____ _____
4x 60 W _____ _____
4x 40 W _____ _____
2x 60 W _____ _____
8 strings x 25 x 7 W _____ _____
Computer _____ 2.5
Monitor _____ 1.6
Scanner _____ 1.5
Laser printer _____ 6.5
Clothes iron 1000 _____
Vacuum cleaner _____ 9.6
Amplifier _____ 1.6
CD Player 15 _____
Portable Stereo 16 _____
VCR 17 _____
TV 150 _____
Water sprinkler Units
2 x .25 amps _____ _____
Electric clocks: 3x6 W _____ _____
Number of appliances with less than 15 amp current rating: _____
Number of appliances with approx. 30 amp current rating: _____
Number of appliances with approx. 40 amp current rating: _____
Equipment with largest amperage rating: ______________________
Cost for the Christmas lights during December: $__________
Cost per year to run the electric clock: $__________
- Patterns and Relations
- Variables and Equations
math to solving problems in another discipline.
- Working with formulae, especially one involving a radical.
- Isolating a variable - in terms of other variables.
- Use community resources to solve problems.
Basic number operations.
- Basic algebra skills.
- Knowledge of scale drawings.
standard writing paper
- large graph paper
- ruler and calculator
Solutions to Principles Section A
How much power is needed to supply the three
houses using 400 amp/ 120 volt service? Convert your answer to
watts = amps x volts
A x V = W
400 x 120 x 3 = 144,000 Watts
144,000 / 1,000 = 144 kW
What is the total power required for all 13
houses in the subdivision?
144 kW + 240 kW = 384 kW
Solution to Principles Section B
Which of three fuses, 20, 23 or 25 amp, do
you use in the transformer for the shopping mall?
To calculate the current (amp), you must
solve the equation for current. Therefore:
power (volt-amp) = Sq. root 3 x
voltage x current
1,000,000 = Sq. root 3 x 25,000 x current
To isolate the variable Current, use basic
algebra techniques to rewrite the formula as:
1,000,000 / sq. root 3 x 25,000 =
23.09 amps = current
You would choose the 23 amp fuse to offer
circuit protection. (Note that you round down to the nearest whole
number.) If you selected a fuse with higher rating, you have endangered
the safety of the mall!
Solution to Learn
warehouse: 35.8 amps (35 amp fuse)
Shopping mall: 115.7 amps (115 amp fuse)
Truck manufacturer: 185.2 amps (185 amp fuse)
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