Answer
$R = 121.60 Ω$
Work Step by Step
Given:
A cylindrical silicon specimen 7.0 mm (0.28 in.) diameter and 57 mm (2.25 in.) in length in which a current of 0.25 A passes in an axial direction. A voltage of 24 V is measured across two probes that are separated by 45 mm (1.75 in.)
Required:
resistance over the entire 57 mm (2.25 in.) of the specimen
Solution:
Using Equations 18.2 and 18.4:
$R = \frac{ρl}{A} = \frac{l}{σA} = \frac{l}{σπ(\frac{d}{2})^{2}}$
$R = \frac{(57 \times 10^{-3} m)}{[12.18 (Ω-m)^{-1}](π)(\frac{7 \times 10^{-3} m}{2})^{2}} = 121.60 Ω$