5. The largest piece of gold ever found had a mass of about70kg. If you were to

Question

5. The largest piece of gold ever found had a mass of about70kg. If you were to draw this mass of gold out into a thin wirewith a cross-sectional area of 2.0mm2, the wire wouldhave a length of 1813km. The wire would also have a resistance perunit length of 1.22x10-2 /m. a. What is the resistance of the wire? b. Suppose the wire were cut into pieces having resistance ofexactly 1/2, 1/4, 1/5, and 1/20 of the wire's resistance ,respectively. If these pieces are reconnected in parallel, what isthe equivalent resistance of the four pieces? 5. The largest piece of gold ever found had a mass of about70kg. If you were to draw this mass of gold out into a thin wirewith a cross-sectional area of 2.0mm2, the wire wouldhave a length of 1813km. The wire would also have a resistance perunit length of 1.22x10-2 /m. a. What is the resistance of the wire? b. Suppose the wire were cut into pieces having resistance ofexactly 1/2, 1/4, 1/5, and 1/20 of the wire's resistance ,respectively. If these pieces are reconnected in parallel, what isthe equivalent resistance of the four pieces?

Explanation / Answer

mass m = 70 kg area of cross section A = 2 mm ^ 2                                    = 2 * 10 ^ -6 m ^ 2 length L = 1813 km             = 1813000 m resistance per unit length  r = 1.22x10-2 /m resistance of the wire R = L r                                     = 1813000 m * 1.22 * 10 ^ -2 / m                                     = 22118.6 (b). resistance of piece when it cut into 1 / 2 is R ' = R /2                                                                              = 11059.3 resistance of piece when it cut into 1 / 4 is R " = R / 4                                                                       = 5529.65 resistance of piece when it cut into 1 / 5 is R"' = 4423.72 resistance of piece when it cut into 1 / 20 is R""= 1105.93 let the resultant of R' , R " , R "' , R"" be  X when connected in parallel then ( 1/ X ) = ( 1 / R ' ) + ( 1/ R " ) + ( 1/ R"' ) + ( 1/R"" )     So, X = 713.5

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