A contractor plans to use a long copper extension cord to supply power from a 120 V household outlet to an electric saw that draws a constant 10 A during operation. The cord consists of two identical copper conductors (one outgoing, one return). Each conductor is a solid cylinder 2.05 mm in diameter. For safety, the contractor requires that the total voltage drop along the entire round-trip length of the cord not exceed 5.0 V when the saw is running. The resistivity of copper at room temperature is 1.68×10−8Ωm.
(a) Calculate the maximum total resistance that the pair of conductors (outgoing + return) may have so that the specified voltage drop limit is not exceeded.
(b) Determine the greatest allowable one-way length of the cord that satisfies the contractor’s requirement.
(c) For the length found in part (b), compute the rate at which electrical energy is dissipated as thermal energy in the cord itself while the saw is operating.
(d) During prolonged use the copper conductors warm up, increasing their resistivity by 10 %. For the length found in part (b), calculate the new voltage drop across the cord under the same 10 A load. Comment briefly on whether the contractor’s original specification is still satisfied.