A room has A.C. run for 5 hours a day at a voltage of 220V. The wiring of the room consists of Cu of 1 mm radius and a length of IO m. Power consumption per day is 10 commercial units. What fraction of it goes in the joule heating in wires. Calculate power loss if the wiring is made of aluminium of the same dimensions `[p_(cu) = 1.7 xx 10^(-8)Omegam, p_(Al) = 2.7 xx 10^(-8) Omegam]`

Options

A. 0.0032
B. 0.0052
C. 0.0064
D. 0.0072

Answer

A

Explanation

Power consumption = 2 units/hour = 2KW
= 2000 J/s
`I=P/V=2000/220=9A`
Power loss in wire = `RI^(2)J/s`
`=pl/AI^(2)=1.7xx10^(-8)xx10/(pixx10^(-6))xx81J/s`
`=4J//s`
`=0.2%`
Power loss in AI wire =`4(p_(Al))/(p_(Cu))=1.6xx4`
= 6.4 J/s = 0.32%