Question

5. The instructions for an electric lawn mower suggest that a 20 gauge extension cord ( cross sectional area = 5.2 x 10-7 m²) should only be used for distances up to 35 m. For longer distances a 16 gauge extension cord should be used ( cross sectional area = 13 x 107 m² ). The resistivity of copper (used in the extension cord) is 1.72 x 10-8 2.m at 20°C and the temperature coefficient of resistivity of copper is 0.004041 (°C). a. What is the resistance of a 20 gauge extension cord of length 25 m at 20°C? b. What is the resistance of a 20 gauge extension cord of length 80 m at 20°C? c. What is the resistance of a 16 gauge extension cord of length 60 m at 40°C?

Answer 1

Crostechial area of 20 gauge externen und As 5:2X10 m revistivity (1) - 1.72x100 m at 2006 coefficient (0) = 0.004041 °C temperature at Now, length of 20 garage extension could , l = 25m i desistance, Rald A to & R - 1042 x 108 x 25 & 2 5.2 x 107 » R = 8.27 x 10 = (0.827 2 by Now length, ea som & Roll = 1072*108x80 5.28107 - Q. 652 I Now, now, crossectional area of 16 gauge extension, A = 13x10 + im Meristoty at 20°c, sr 1.72X108 om temp. coefficient, da 0.000041 length l = bom first we have to cačulate resistivity at 40°c we know that id - Pue - Seo Pro ( 12 ) we have so = +72X108 um Tuo = 40 c and Too = 20°c Now butting the value - 0.0olour = luo - 1*72x108 - lo-1-72x108 10242x 108 x (40-20) 1.728108 x 20 > Divoll ou 1 X1924109 x 20 = fuo - 1272x168 » 0-138x108 - Suo - 1724103 » Pro = 0.138810 +1.728108 = 1.8588108 am Now, Resistame, R - S xe - 1-858010 8Go - 0.85802 A 13x107 Honce resistance R = 0.858 21