In a home lights draw 20 A and are on 10 hrs every day lamps

In a home lights draw 20 A and are on 10 hrs every day, lamps are about 100 ft from wiring panel. 12 gauge wire carries enough current but you are considering whether to buy 10 gauge wire to save money as potential lower wire loss. Assume \"Romex\" wire (2 wire + ground) costs $0.50 per ft for 12 gauge and $0.70 per ft for 10 gauge, and utility rates are $0.10 per KWh. how many years (simple payback period) would it take to pay the extra cost of heavier duty wire?

Solution

Given that home lights draw I_L = 20 A of current for T = 10 hrs every day;

Energy consumed by these lights per day is E_L = 120*20*10 = 24 kWH/day

Cost of Electrical energy utilized is C = E_L * 0.1 = 24*0.1 = 2.4 $/day

Distance between lights and wiring panel is L = 100 ft .

Cost 12 gauge wire per ft is C₁₂ = 0.5 $/ft for 100 ft C_T12 = 100*0.5 = 50 $

Cost 10 gauge wire per ft is C₁₀ = 0.7 $/ft for 100 ft C_T10 = 100*0.7 = 70 $

extra cost is 20 $;

Energy lost if 12 guage wire installed is = I_L² * R₁₂ * T *L= 20²*1.588*10^-3 * 10 * 100 = 0.635 kWH

Cost due energy lost per day = 0.635*0.1 = 0.0635 $/day

Energy lost if 10 guage wire installed is = I_L² * R₁₀ * T *L= 20²*0.9989*10^-3 * 10 * 100 = 0.399 kWH

Cost due energy lost per day = 0.399*0.1 = 0.0399 $/day

Now extra cost paid if 12 gauge wire installed instead of 10 guage is 0.0635 - 0.0399 = 0.0236 $/day

Pay back period of extra cost if 10 gauge wire is used instead of 12 gauge wire is = 20/0.0236 = 847.45 days

or 847 days or 2 years 2 months 14 days.

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