*Note* In this material, much emphasis is placed on definitions and correct use of units (centimetres, Watts, litres, and so on). The reason is simple: All practical applications of Mathematics are meaningful only if appropriate units are used.

THE ELECTRIC METER

Electricity is supplied to your house either through overhead or underground wires. In either case these wires pass through an electric meter so that the utility company can determine your monthly consumption of electric energy.

In apartment blocks the meters are usually located in a "meter room".

The meter has five dials. In three of these the pointers rotate clockwise. Study the illustration and understand why the reading here is 43231. The unit is the kWh, or kilo-watt-hour. Kilo means 1000, Watt-hours are units of electric energy.

Notice that the "k" and the "h" are lower case while the "W" is capitalised. In the metric system of measurements, those units that are named after people - the Watt is named after James Watt, the inventor of the steam engine - are capitalised. Other units are not capitalised.

Once every month or two a meter reader come by to read the meter. The reading the last time the reading was taken is subtracted from the present one and the result multiplied by the rate to determine your monthly bill. Here is a copy of one of my bills:

At the end of this two-month billing period the meter reading is ..... The previous meter reading was......, and so I am beeing billed for ...... kWh.

The rate at which I am being charged is ..... per kWh. By the way, this rate is very low compared to most other places.

In addition the is a basic charge for each billing period is ....; and then there is GST.

In the period April - May I consumed electric energy at a rate of approximately ..... kWh per day. This is ...... (more or less) than for the same period last year.

The various electrical appliances in your home use different amounts of energy. The unit for the rate at which electrical energy is used is the Watt (W) or the kiloWatt (kW).

For example, most electric ligh bulbs are rated at 100 W. This means that these bulbs use 100 W-h (Watt-hours) of electric energy every hour. Here is how you calculate the cost of burning a 100 W lightbulb for 24 hours a day for a whole month:

Total energy used = Rate of energy usage * time
                  = 100 W * 14 hrs/day * 30 days/month

                  = 42000 W-h = 42 kW-h

Cost = energy * rate = 42 kW-h * $0.06 / kW-h
                     = $2.52

That doesn't seem like a lot; but here is a table showing the cost of using a typical selection of electrical appliances:

Appliance	Rate of consumption	Hours /day	Energy used / day	Energy used / month	Monthly cost
Dryer	3 kW	4 hrs	12 kW-h	360 kW-h	$21.60
Baseboard	1.5 kW	10 hrs
Television	600 W
Hot Water	3 kW	*

It is difficult to judge how many hours per day that your hot water is being heated. The cost of hot water can be significant and is discussed in another section.

The rest of this table is left blank for you to do some investigating with. See if you can account for your family's electric bill.

ELECTRIC VOLTAGE AND CURRENT

Here are two commonly used batteries. One is 9 Volts, the other is 6 Volts.

When a battery is connected to a lightbulb, the filament inside will glow provided the voltage of the cell or battery is great enough to overcome the resistance of the filament, allowing a current to flow in it.

Flashlight bulbs are normally designed to work with 3, 6 or 9 Volts. If any of these are connected to a car battery, the bulb will burn out very quickly because the current resulting from 12 V will be so high that the filament will vaporise.

The unit for measuring current is Ampere, sometimes called amps. If a curent of 1 A flows in a 3 V flashlight bulb, then the bulb is using energy at a rate of 3 W.

Rate of energy consumption (Watt) = electric pressure (Volt) * current (Ampere)

in this case:                                   1 W = 3 V * 1 A

Here is another example:            100 W = 110 V * 0.9 A

A word of caution here: Although it is safe to experiment with and measure electricity supplied by flashlight cells and car batteries, NEVER experiment with or attempt to measure the electricty supply in your house. 12 V you can't feel; 50 V you can, and 100 V can kill you. This is serious.

The actual voltage in an ordinary domestic electric circuit varies; but is "supposed to be" about 110 V. Therefore the current in a 100 W lightbulb is a little less than 1 A.

Here is yet another example:         3 kW = 220 V * 13.6 A

The current in a 3 kW electric dryer is close to 14 A. Notice also that an electric dryer is connected to a 220 V circuit

 FUEL COST

The money a person spends on gasoline is a significant portion of the cost of operating a car.

The amount of gasoline that a car uses depends on what kind of car it is, whether it is driven mostly in traffic or on the highway, the driving habits of the owner, the condition of the engine and so on.

Heavy cars with powerful engines that do mostly short trips with many stops and starts in traffic use much more gasoline that light cars used on the highway. Fast acceleration and lots of braking increases fuel consumption.

For the purposes of this discussion, let us talk about a car that averages 30 litres of gasoline for every 100 km driven.

The price of a liter of gasoline varies from place to place, and changes, sometimes from day to day for a variety of reasons. But let us again, for the purposes of the discussion, consider the price of gasoline to be $0.80 per litre. This would, of course, be shown on the pump as being 79.9 cents - which is the same thing as $0.80!

The distance that a person drives per year also varies a great deal, but many people drive 15,000 km/year. Fuel cost in this example would be

15,000 km/yr * 30 l/100 km * $0.80 /l = $3,600 per year, or $300 per month, or $10 per day.

BUYING A CAR

Owning a car involves other expenses besides gasoline costs. Repairs, maintenance (occasional replacement tires, oil changes and so on), insurance and licensing. One expense that most people don't even consider is the cost of the money that you have "invested" in the car.

The cost of this "investment" varies a great deal with the cost of the car and also the changing rates of interest charged on borrowed money. Let us do a calculation based on some reasonable assumptions:

Let us pretend that you borrow $15,000 to buy a modest car. You have to pay 10% interest, let's say. That is more than the "going rate" today - but not by much.

10% per year on $15,000 = 0.1 / month / 12 months / year * $15,000 = $120 per month in interest.

That's for the first month. You will be paying back some of the amount borrowed, of course, so that the next month you don't owe as much... and so on. In the next section we show you about something called spreadsheets. With a spreadsheet is possible for you to calculate exactly how much will be paying for having this car - and how much you could save if you took the bus!

SPREADSHEETS

A spreadsheet is a commonly available computer program that simplifies all sorts of useful calculations. Here we will do a simple illustration of how a spreadsheet works, using the example of the car payments just mentioned in the last section.

We assume you have access to a computer and a spreadsheet program like Excel or Appleworks.

The spreadsheet consists of a number of cells labelled A1, A2,.... B1, B2..... and so on as shown here. Each cell can contain either text, a number, or a formula.

In this illustration we have entered text into cells, A1, A2, A4, B4, C2, C4, B4, E2, and E4; numbers cells A5, B2, D2, and F2; and formulas into the cells with the "=" signs.

The formula in cell B5 "tells the computer" copy the number in cell B2. Cell B5 therefore has the number 15000 in it.

The formula in cell C5 says that in this cell we want whatever is in cell B5 multiplied with whatever is in cell D2. So here we would expect to have 15000 * 0.1 / 12 = 125

The formula in cell D5 says that here we want a copy of F2 which is 300.

The formula in cell E5 says that here we want a number which represents what we started with (15000) + interest (125) - payment (300) = 14825

Spreadsheets have two views - -me in which the formulas show, and the other in which the calculated results show. Here is what the spreadsheet looks like in the other view:

As you see, the calculations we have mentioned have been made by the spreadsheet program.

Now look at this formula view:


We could explain the additional formulas - but it would be more interesting for you to work this out yourself! What we have done also is to extend the calculations for four years(*). In any event, when the calculated results are shown it looks like this:

As you can see, $300 per month is not enough to pay off this car in four years (* there is a slight error being made here... see if you can fix it)

When and if you set up your own spreadsheet you can experiment by changing the number in cell F2 and in this way you can discover how large your payments would have to be to pay off the loan in whatever length of time you choose. You can also experiment with the interest rate and so on. This is a very useful exercise because it allows you to determine exactly how much you are paying for the privilege of buying in credit.