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A family of four uses two tubs, one dishwasher, and one clothes washer in their home. Suppose an electric water heater supplies the hot water for the usage points. Determine:
(a) The usage points for this home
(b) The gallon capacity for the usage points
(c) The ratiing of the heating elements of the electric water heater
(d) The current flowing through the heater
(e) The correct-size wire to use when the electric water heater is installed.
The strings:
S7P3A32 (force - push).
The math:
Pj Problem of Interest is of type force (push).
(a) Usage point is calculated by assigning one usage point per person in the home, and one usage point for point of usage of hotwater in the home (bathtub/shower, dishwasher, clothes washer, etc). The total usage points is used to determine the amount of water in gallons from a usage points table.
So, 4 members of the family = 4 usage points
2 tubs, 1 dishwater, 1 clothes washer = 4 usage points
So, total usage points = 8 usage points.
(b) a typical usage points table is as follows:
| Usage Points | Gallons Of Water |
| 4 or less | 40-galon water heater |
| 5 or 6 | 50-gallon water heater |
| 7 or 8 | 65-gallon water heater |
| 9 or more | 80-gallon water heater |
So, from usage points table, water heater for the home will have a 65-gallon capacity.
(c) A standard 65-gallon water heater has its heating elements rated at 4,500 watts and 240-volt AC wiring.
(d) If P = 4500 W, and V = 240 volts I = 4500/240 = 18.75 A.
(e) Wire diameter, current capacity, volts, and power table. Continuous load assumed.
| American Wire Guage | Ampacity (current capacity) | Volts - Wattage |
| 18 | 7 Amperes | 24 Volts - 134 Watts |
| 16 | 10 Amperes | 24 Volts - 192 Watts |
| 14 | 15 Amperes | 120 Volts - 1,440 Watts |
| 12 | 20 Amperes | 120 Volts - 1,920 Watts; 240 Volts - 3,840 Watts |
| 10 | 30 Amperes | 120 Volts - 2,880 Watts; 240 Volts - 5,760 Watts |
| 8 | 40 Amperes | 240 Volts - 7,680 Watts |
| 6 | 60 Amperes | 240 Volts - 9,600 Watts |
Calculated current I = 18.75 Amperes.
So, from the wire-gauge table, a 12-gauge wire can carry 20 amperes. Since the calculated current is less than 20, it would seem appropriate to select a 12-gauge wire. However, the wattage rating of the electric water heater is 4,500 watts which is significantly more than the 3,840 watts of the 12-gauge wire. So a 10-guage wire is the appropriate wire to use when the electric water heater is installed.
The point . is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.
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