Calculations
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A transformer is a device that changes or transforms alternating current of one voltage to alternating current of another voltage.  Transformers used in building work consist essentially o iron core on to which two coils: a primary coil winding and a secondary winding coil.  A voltage impressed on the primary coil induces a voltage in the secondary coil in proportion to the ratio of turns in the coils.  Thus a step down transformer has a larger number of turns in its primary winding than in its secondary coil.  Transformers are available in single phase or three phase construction.  Transformer power capacity is rate kilo-volt amperes (kVA). 

OHM's Law

The electrical relationship between voltage, current, and impedance is called Ohm's law.  Ohm's law is a simple mathematical formula which says the voltage in a circuit can be computed by multiplying the current flowing in the circuit times the impedance of the circuit.  The "impedance" of a circuit is measured in ohms and is represented by the letter Z.  The term impedance is used to include both inductive and capacitive reactance and resistance because all three are forms of opposition to the flow of current.

Ohm's Law is written as V = A x Z where

V = voltage (volts)
A = current (amps)
Z = impedance (ohms)

The electrical impedance of a circuit is made up of both the electrical resistance and the electrical reactance of the elements in the circuit. Both the resistance and reactance impede the current flow through a circuit.

Resistance loads include incandescent light bulbs and electric heating elements. Reactive loads include electric motors and other devices where the magnetic field created around a coil of wire or in a capacitor is utilized as electrical energy.

 

Resistive Loads

In AC and DC circuits containing purely resistive loads, like lights and heaters, Ohm's Law can be used to compute current, voltage and resistance in the circuit.

In a resistive DC circuit, both current and voltage are fixed, steady values.

In an AC resistive circuit, the current alternates exactly in step with the voltage. In either case, Ohms Law can be applied.

In a resistive circuit Ohm's Law states that: voltage is equal to current times resistance.

Ohm's Law V = A x R where:

V = voltage (volts)
A = current (amps)
R = resistance (ohms)

 

For example, a current of 2 amps flowing through a resistance of 3 ohms is said to produce a voltage "across" that resistance of 6 volts.

Reactive Loads  

The current and voltage in AC circuits that contain inductors, capacitors, or both, behave much differently than in a purely resistive circuit. We cannot measure resistance directly in these circuits. We measure what's known as "reactance."

Inductors and capacitors react to current flow in ways that oppose, or impede, changes in the flow of current, but they do it in a different fashion than a pure resistor. Each device has its own characteristics, which creates an impeding force.

Whenever there is an inductor, or coil, in a circuit, we call its impeding force to current flow "inductive reactance." For a circuit with a capacitor, the impeding force is called "capacitive reactance."

We treat both resistance and reactance as impedance, that is, any opposition to changes in the flow of current.

 

 

Fuel Cost Adjustment/Fuel Charge - How To

 

You can calculate the cost of energy use for various electrical appliances and equipment if you have these three pieces of information:

The rated power of the appliance, usually given in watts;
The length of operating time,
And the cost of electricity.

The rated power, in kilowatts, is multiplied by the operating hours to determine the energy use in kilowatt-hours. The energy use is then multiplied by the electric rate to determine the cost of electricity to run the appliance.

For example, let's determine the cost to run a 1,500-watt heater for six hours based on an electricity cost of eight cents per kilowatt-hour.

The power rating of the heater is 1,500 watts.  To convert this to kilowatts, divide 1,500 watts by 1,000.  This yields 1.5 kilowatts. Now multiply the power use, 1.5 kilowatts, by the operating time of 6 hours; which equals 9 kilowatt-hours of energy use. Finally, multiply the 9-kilowatt hours of energy use times the electric rate of eight cents per kilowatt-hour. You now know it costs 72 cents to operate the heater for 6 hours.

On larger appliances, like refrigerators and water heaters, there is a yellow label on the side which states how much energy costs to run the appliance for a year. If you look closely you can see that the manufacturer has used "averages," family size, hours per day, etc, to determine the annual operating costs for this appliance.

Energy Use = Power x Time

KWh = kW x Hours

Then:

 

Operating Cost ($) = Energy Use (kWh) x Electric Rate

 

While electrical power measured in kilowatts is important to the people who design and size the electrical system, most consumers are more interested in the amount of electrical energy that is used in their house, or by a single appliance. The term used in measuring electrical energy is the "kilowatt-hour." This is a measure of the amount of electrical power used in one hour. Kilowatt-hours are what the electric meter on the side of your house measures. This is the basis for calculating your monthly electric bill.

Once you know the energy use of any appliance, you can figure the cost to run that appliance. There are three methods of finding the amount of electrical energy being used by a piece of equipment.

They are:

1. Estimating wattage and time;
2. Using the kilowatt-hour meter;
3. And installing a check meter.

 

Determining kW Use

Estimating

You can estimate the power use in kilowatts of an appliance from the nameplate information. If the nameplate indicates the appliance's rated wattage to be 1200 watts at 120 volts, then divide the wattage by 1000 to convert to the kilowatt power usage. If you've been curious what a 100-watt light bulb uses in kilowatts, divide 100 by 1000 and get 0.1 kilowatts.

Meter-Disk Revolutions

The power used by an appliance can be measured by observing the meter-disk revolutions on the regular kilowatt-hour meter at the service entrance. This method has the advantage of accurately measuring the watts or watt-hours used by equipment under actual loading and service conditions. This method can also be used to measure the power use of the service, or for any desired number of combinations of loads operating at one time. 

Every regular kilowatt-hour meter has a flat aluminum disk with a black mark along its edge. This disk turns when energy is being used by the service. Meters also have a meter constant called the K sub h, which is shown on the meter nameplate. This K sub h constant indicates how many watt-hours are used for each revolution of the meter disk. A constant of "Kh = 7.2" means that for each revolution of the disk, 7.2 watt-hours of energy have been used.  The actual number associated with the constant will vary with different meters. Common values are 3.6 and 7.2.

To determine how much power is used by counting meter-disk revolutions, proceed as follows:

1. Make sure the appliance to be checked is the only operating device on the service. This may require finding the circuit that supplies the appliance you wish to check in the breaker box and shutting off all the other breakers. This assures that the appliance will be the only device operating and using electricity.

2. Disconnect, or power off, any other equipment that is on the same circuit with the appliance to be checked.

3. With a watch, determine the time it takes for the meter-disk to make a certain number of complete revolutions. Choose any number of disk revolutions you desire. Depending on the appliance you're measuring, the number of revolutions will vary. If you are measuring a smaller, less power consuming device, the time to move the disk may be quite lengthy. There is also the issue of devices like refrigerators and air conditioner compressors that cycle on and off. Make sure you measure these appliances while they are on, not when they have cycled off.

4. To calculate the kilowatts of power used by the appliance, divide the number of disk revolutions by the time in seconds. Multiply this times 3.6 and multiply again times the K sub h factor from the meter. This is the amount of power actually used by the appliance in kilowatts.

As an example, the meter was timed with everything off in the house except the air conditioner. The meter disk made 10 complete revolutions in 30 seconds and the k sub h on the meter was 7.2. The power use, in kilowatts, of the air conditioner is found by dividing 10 revolutions by 30 seconds, multiplying this times 3.6 times 7.2, which equals 8.6 kilowatts.  Remember, though, an air conditioner doesn't run all of the time - it cycles on and off.

 

Electric Rates/Prices

Electric rates, the cost of energy per kilowatt-hour, vary from utility to utility; by rate class within a utility, and sometimes even by the time of day or the season of the year. Each power supplier has established rate schedules that are usually approved by regulatory agencies for a given customer type.

The base electric rate is applied to the number of kilowatt-hours consumed during a billing period, approximately a month long, to determine the electric bill. T he billing period will usually not be the same as the calendar month and the meter may run 30 to 32 day intervals - and not on exactly the same day of each month.

Other charges may be added to the base cost of electricity. These may include a charge for minimum monthly service, demand charges on larger customer accounts, fuel adjustment charges, other surcharges, power factor penalties and taxes. Rates charged in the summer months may differ from those charged during the winter. Special rates may be offered for customers who agree to let the power supplier cycle equipment on and off such as electric heaters or air conditioners during high use times of the day or year.  All of these charges and their application are covered under "Electric Bill Components."