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 2.28 mm. The other wire is composed of 19 strands of thin copper wire bundled together. Each strand has a circular cross section of radius 0.456 mm. The current density J in each wire is the same. J = 3750 A /m^2

a. How much current does each wire carry?
b. What is the resistance of a 6.25 m length of each wire?

Answer with Explanation:

We are given that

Radius of  solid core wire=r=2.28 mm=

Radius of each strand  of thin wire=r'=0.456 mm=

Current density of each wire=

a.Area =

Where

Using the formula

Cross section area of copper wire has solid core =

Current density =

Using the formula

Total number of strands=19

Area of strand wire=

b.Resistivity of copper wire=

Length of each wire =6.25 m

Resistance, R=

Using the formula

Resistance of solid core wire=

Resistance of strand wire=

multiple

answera compound;