Question

1. A carbon wire with a 3 mm diameter has a resistance of 100 ohms. How long is the wire?

2. A 200 m long aluminum wire has the same resistance and cross sectional area as a carbon wire. What is the length of the carbon wire?

3. A wire made of an unknown substance has a resistance of 125 mΩ. The wire has a length of 1.8m and a cross-sectional area of 2.35 x 10^-5 m^2. What is the resistivity of the substance from which the wire is made? Give your answer in scientific notation to one dicimal place.

Answer 1

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

Resistivity of carbon $=1×10^{-5}\Omega\>m$

Resistivity of Aluminum $=2.8×10^{-8}\Omega\>m$

1.

$l=\frac{100×\pi(\frac{3}{2})^2×10^{-6}}{1×10^{-5}}$

$=70.69m$

2.

$R=\frac{2.8×10^{-8}×200}{A}=\frac{1×10^{-5}×l}{A}$

$l=0.56m$

3.

$\rho=\frac{125×10^{-3}×2.35×10^{-5}}{1.8}$

$=1.6×10^{-6}\Omega\>m$