Download The Electric Bill

Dr. G.H. Massiha and Alan Smith
Department of Industrial Technology
The University of Louisiana at Lafayette
Lafayette, LA 70504
Tel. (337) 482-5719
Fax (337) 482-6661
[email protected]
The Electric Bill
Determining Watts and Kilowatthours. It is extremely helpful to know how to
determine watts and kilowatthours. This knowledge is valuable when estimating the
cost of operation of a new piece of equipment or in determining whether or not an
appliance is functioning properly. It also makes one a better judge of the relative value
of electrical appliances and increases the over-all understanding of electricity. Finally,
and perhaps most important of all, this knowledge often results in a greater
appreciation of the value received from the electric-energy dollar. Since power is the
rate at which energy is used, power utilized over a period of time represents energy
consumption. If you multiply power in watts and time in seconds, you have energy in
joules, symbolized by W.
W = Pt
Because power companies deal in huge amounts of energy, the most practical unit is
the kilowatt-hour (kWh). You use a kilowatt-hour of energy when you use the
equivalent of 1000 W of power for 1 hr. For example, a 100 W light bulb burning for 10
hr uses 1 kWh of energy.
W = Pt = (100 W)(10 hr) = 1000 Wh = 1 kWh
There are several methods for determining the amount of energy used by an
appliance:
Method 1. Nameplate Data. The nameplate provides the equipment
manufacturers with a means of conveying to the customer the rated
electrical values and output capacities of the equipment. The nameplate
may be a separate metal plate securely fastened to the equipment or it
may be stenciled, stamped, or otherwise labeled directly on the
equipment frame. The input voltage for which the equipment was
designed is always given and the input watts, if not given, can be
obtained by calculation. Various other data are included, depending upon
the type of equipment in question. Several nameplates are shown in
Figure 1.
The wattage rating on the nameplate is interpreted as that value
of watts used by the equipment when it is connected to its rated voltage
and is operating at full capacity. For example, suppose an electric iron
has a nameplate rating of 600 watts, 120 volts. This iron converts
electrical energy at a rate of 600 watts when it is connected to 120 volts.
In order to determine the kilowatthours it is necessary to know the hours
of operation. For 4 hr of operation, 2.4 kWh is required (600 X (4/1,000)).
Occasionally the nameplate data include only the volt and the
ampere rating. For farm equipment, other than motors, the watts are
calculated by multiplying the volts by the amperes. If two, voltage and
two current values are given, multiply the largest value of one by the
smallest value of the other.
The power to an electric motor cannot be obtained by multiplying volts and
amperes because the power factor of a motor is not 100 percent. A practical value for
the power input to a motor is obtained by:
a.
Multiplying 1,200 by the horsepower rating of the motor if the motor is
smaller than ½ hp.
GE Long Life Light Bulb
100 Watt
120 Volts
Nameplate on Light Bulb
SONY
Model CFD-Z500
120 Volts AC or DC
15 Watts
Label on table-model radio
AC Only
1200 Watts
120 Volts
Model 17109R
Nameplate on an electric iron
Figure 1. Samples of nameplates found on electrical equipment.
b.
Multiplying 1,000 by the horsepower rating of the motor if the motor size
is ½ hp or greater.
The amount of energy required depends upon the operating time.
Example 1. Determine the kilowatthours used for operating two motors at their rated
capacity for 20 hr. The ratings of the motors are 1 and ¼ hp.
1,000 x 1 = 1,000 watts
1,200 x ¼ = 300 watts
1,300 watts
1,300 x 10 = 13 kWh
1,000
Method 2a. Voltmeter and Ammeter. The power used by an appliance with a
large resistance such as light bulbs, irons, and toasters can be measured with the aid of
a voltmeter and ammeter.
Figure 2. Analog AC voltmeter and digital AC ammeter connected to a space heater.
Method 2b. Wattmeter. The power usage by an appliance that uses motors can
be measured with the aide of a wattmeter. When the consumer desires to know the
exact amount of energy used by a certain appliance, he should request the power
supplier to install a check meter. This meter is exactly the same as the regular
kilowatthour meter. The kilowatthour value is read as described in the preceding
section. If the number of watts is desired, multiply the kilowatthour readings by 1,000,
then divide by the number of hours the appliance is on.
115-volt source
The larger terminals
are ammeter terminals
Appliance being tested
(including motors)
This meter is a combination
of ammeter and voltmeter
Figure 3. Analog Wattmeter and an AC motor
Method 3a. Meter-disk Revolutions. This method makes use of the regular
kilowatthour meter that is installed on houses for recording the number of kilowatthours
used each month. The meter’s Kh factor and metal disk are the significant items
employed and these, together with a watch or clock, are all that is needed. The Kh
factor is printed on the nameplate of the meter as shown in Figure 3 and for farm-type
meters ranges from 1.5 to 5.0. For a particular meter the Kh value is constant. It is
equal to the number of watthours per revolution of the disk. The disk revolutions are
counted for a definite length of time (6, 10, or 12 min.) and the watthours are obtained
by calculation. Figure 5 shows how to read the values from the dials on a kilowatthour
meter. All appliances except the one being tested must either be disconnected
Figure 4. Front view of kilowatthour meter. The Kh factor is shown on the nameplate.
The first reading is 3,257 kWh and the second reading is 3,293 kWh.
Figure 5. How to read the dials on a kilowatthour meter.
or turned off. The desired values are obtained from these relationships:
Watthours = Kh x no. of revolutions
Watthours per hr = watthours x 60
min of count
Watts = watthours per hr
Example 2. All electrical equipment is off, except an electric motor. The
kilowatthour-meter-disk revolutions are counted for a period of 6 min. The disk makes
20 revolutions and the Kh factor of the meter is 2.5. Determine the kWh that would be
used by this motor if it were operated for 1 hr. What is the power input to the motor?
Watthours = Kh x revolutions = 2.5 x 20 = 50
Watthours per hr = 50 x (60/6) = 500
kWh = 500/1000 = 0.5
Power input to the motor = watts = 500
Method 3b. This type of meter does not have dials like the above meter. To
calculate the energy used over a period of time, take an initial reading from the meter,
wait the specified period of time, and record the second reading. To calculate the
kilowatthour usage, subtract the initial reading from the second reading and that value is
the amount of energy used for that specific period.
Figure 6. Kilowatthour meter.
Listed below are some problems to calculate the power input to:
A. An electric heater that draws 6 amp when operating from a 115-volt source.
B. A lamp that draws 0.52 amps from the 115-volt source.
C. A heater operating from the 230-volt source and having a resistance of 46
ohms.
Conclusion
Being able to calculate power and energy will allow students to check the energy
being consumed by the devices that are used in everyday tasks. Three different
methods for calculating power and energy are shown. From these methods students
will begin to understand the relationship that power, energy usage, and money have
with each other.