Two insulated copper wires of similar overall diameter have very different inter

Question

Two insulated copper wires of similar overall diameter have very different interiors. One wire possesses a solid core of copper, with a circular cross-section of radius 1.53 mm. the other wire is composed of 19 strands of thin copper wire bundled together. Each strand has a circular cross-section of radius 0.306 mm. the current density in each wire is the same: J = 2950 A/m^2 How much current does each wire carry? resistivity of copper is 1.69 times 10^8 Ohm m. What is the resistance of a 4.00 m length of each wire?

Explanation / Answer

Current = current density x cross sectional area

a.) Current through the solid wire = J x area of solid wire

current through the solid wire = J x R2  = 2950 x (1.53x 10-3 )2 = 0.02169475502 A

Current through the stranded wire = J x area of strands

current through the stranded wire = J x 19 x r2 = 2950 x 19 x ( 0.306 x 10-3 )2 = 0.01648801381 A

b.) resistance = resistivity x length / area of cross-section

resistance of solid wire = 1.69 x 10-8 x 4 /( (1.53x 10-3 )2 ) = 9.192083517 x 10-3 ohms

resistance of stranded wire = 1.69 x 10-8 x 4 / ( 19 x   ( 0.306 x 10-3 )2 ) = 12.09484673 x 10-3 ohms

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