## What considerations determine the maximum current-carrying capacity of household wiring?

According to the U.S. National Electrical Code, the copper wire used for interior wiring of houses, hotels, office buildings, and industrial plants is permitted to carry no more than a specified maximum amount of current. The table below shows the maximum current Imax for several common sizes of wire with varnished cambric insulation. The“wire gauge” is a standard used to describe the diameter of wires. Note that the larger the diameter of the wire, the smaller the wire gauge.

Wire gauge |
Diameter (cm) |
Imax (A) |

14 |
0.163 |
18 |

12 |
0.205 |
25 |

10 |
0.259 |
30 |

8 |
0.326 |
40 |

6 |
0.412 |
60 |

5 |
0.462 |
65 |

4 |
0.519 |
85 |

- What considerations determine the maximum current-carrying capacity of household wiring?
- A total of 4200 W of power is to be supplied through the wires of a house to the household electrical appliances. If the potential difference across the group of appliances is 120 V, determine the gauge of the thinnest permissible wire that can be used.
- Suppose the wire used in this house is of the gauge found in part (b) and has a total length of 42.0 m. At what rate is energy dissipated in the wires?
- The house is built in a community where the consumer cost of electric energy is $0.11 per kilowatt-hour. If the house were built with the wire of the next larger diameter than that found in part (b), what would be the savings in electricity costs in one year? Assume that the appliances are kept on for an average of 12 hours a day.

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Calculus based Physics
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