A conductor has a diameter of 1.00 mm and length 2.00m. if the resistance of the material is 0.1Ω, its resistivity is?
A
2.55 x 105 Ωm
B
2.55 x 102 Ωm
C
3.93 x 10-6 Ωm
D
3.93 x 10-8 Ωm
Verified Correct Answer: D.
Physical Principles & Numerical Solution
R = \(\frac{ \rho \times L}{A}\), \(\rho\) = \(\frac{R . A}{L}\)
d = 1mm = 0.001m, r = 0.0005m
A = \(\pi\)r\(^2\) = \(\frac{22}{7}\) x (0.0005)\(^2\) = 7.857 x 10\(^{-7}\)
\(\rho\) = \(\frac{R . A}{L}\) = \(\frac{0.1 \times 7.857 \times 10^{-7}}{2}\)
\(\rho\) = 3.928 x 10\(^{-8}\)\(\Omega\)m
Source: Myschool Past Questions Archive (Record #14000)