Question

A section of iron wire having a diameter of 0.030 inch is measured to have a resistance of

2500

Ω (at a temperature of 20°C).

a. Determine the cross

-sectional area in square meters and in square millimeters.

(Note: 1 inch = 2.54 cm = 25.4 mm)

b. Calculate the length of the wire in meters.

Answer 1

We know that

$R=\frac{\rho l}{A}$

$l=\frac{RA}{\rho}$

$$l=\frac{2500\times3.14\times(3.81\times10^-4)^2}{9.81\times10^{-8}}=11615.83m$$

Area

$A=\frac{\rho l}{R}$

$$A=\frac{9.71\times10^{-8}\times11615.83}{2500}=4.52\times10^{-7}m^2$$

$A=0.452mm^2$