Question

(a)Compute the electrical conductivity of 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.).(b)Compute the resistance over the entire 57 mm (2.25 in.) of the specimen.

Answer 1

Answer:

a) $\sigma = 12.2$ (Ω-m)^{-1}

b) Resistance = 121.4 Ω

Explanation:

given data:

diameter is 7.0 mm

length 57 mm

current I = 0.25 A

voltage v = 24 v

distance between the probes is 45 mm

electrical conductivity is given as

$\sigma = \frac{I l}{V \pi r^2}$

$\sigma = \frac{0.25 \times 45\times 10^{-3}}{24 \pi [\frac{7 \times 10^{-3}}{2}]^2}$

$\sigma = 12.2$(Ω-m)^{-1}[/tex]

b)

$Resistance = \frac{l}{\sigma A}$

                  $= \frac{l}{ \sigma \pi r^2}$

$= \frac{57 \times 10^{-3}}{12.2 \times \pi [\frac{7 \times 10^{-3}}{2}]^2}$

Resistance = 121.4 Ω