A 10.3 g wire has a density of 10.7 g/cm3 and a resistivity of 6.9 * 10-8 Ω · m. The wire has a resistance of 59 Ω. How long is the wire?

Answer

28.65 m

Explanation

First we need to find the cross sectional area of the wire and for that we need to find the radius of the wire, r

density = mass / volume

10.7 = 10.3 / volume

volume = 10.3/10.7

= 0.96cm³

1,000,000 cubic centimeters = 1 cubic meter

so

0.96/1,000,000 = 9.6 x 10^-7m

formula for volume

volume of wire = πr² (L)

9.6 x 10^-7 = πr² (L)

r = √ (9.6 x 10^-7/π (L))

cross sectional area of wire = πr²

Formula for resistivity

R = p * length / cross SA

59 = 6.9 * 10^-8 (L) / πr²

59 = 6.9 * 10^-8 (L) / π (9.6 x 10^-7/π (L)

59 = 6.9 * 10^-8 (L) / 9.6 x 10^-7 / (L)

59 / 6.9 * 10^-8 = L / 9.6 x 10^-7 / (L)

L² = 59 (9.6 x 10^-7) / 6.9 * 10^-8

L² = 820.87

L = √ 820.87

= 28.65m

So, the wire is 28.65 m long