A multiclad wire consists of a nickel core of radius 2.45 mm surrounded by a cop

Question

A multiclad wire consists of a nickel core of radius 2.45 mm surrounded by a copper sheath of thickness 1.79 mm.What is the resistance of a 14.7 m long strand of this wire?

Table 25.1 The Resistivity and the Temperature Coefficient of the Resistivity for Some Representative Conductors Resistivity, at 20 °C (10-8 m) Temperature Coefficient, (10-3 K-1) Material Silver Copper Gold Aluminum Brass Tungsten Nickel Iron Steel Tantalum Lead Constantan Stainless steel Mercu Nichrome 1.62 1.72 2.44 2.82 3.9 5.51 3.8 3.9 3.4 3.9 4.5 5.9 9.7 5 3.1 4.3 0.01 49 70 95.8 108 0.89 0.4

Explanation / Answer

for nickel

area of cross section = A1 = pi*(R2^2-R1^2)

R1 = 2.45 mm = 0.00245 m

R2 = R1 + t = 0.00245+0.00179 = 0.00424 m

length = L1 = 14.7 m

resistance = R1 = rho1*L1/A1 = (7*10^-8*14.7)/(pi*(0.00424^2-0.00245^2)) = 0.02735 ohms

for copper

area of cross section = A2 = pi*R1^2

langth = L2 = 14.7 m

resistance =R2 = rho*2*L2/A2 = (1.72*10^-8*14.7)/(pi*0.00245^2) = 0.01341 ohms

1/R = 1/R1 + 1/R2

1/R = 1/0.02735 + 1/0.01341

R = 0.008998 ohms

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