Materials Science and Engineering: An Introduction

Published by Wiley
ISBN 10: 1118324579
ISBN 13: 978-1-11832-457-8

Chapter 18 - Electrical Properties - Questions and Problems - Page 778: 18.1b

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: $R = \frac{ρl}{A} = \frac{l}{σA} = \frac{l}{σπ(\frac{d}{2})^{2}}$ $R = \frac{(57 \times 10^{-3} m)}{[12.18 (Ω-m)^{-1}](π)(\frac{7 \times 10^{-3} m}{2})^{2}} = 121.60 Ω$
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