Answer to Question #308925 in Physics for Hatdog

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

1.

$$l=\frac{RA}{\rho}=\frac{100*3.14*0.003^2/4}{3.5*10^{−5}}=20\:\rm m$$

2.

$$l_C=l_{Al}\frac{\rho_{Al}}{\rho_{C}}=200*\frac{2.65*10^{−8}}{3.5*10^{−5}}=0.15\:\rm m$$

3.

$$\rho=\frac{RA}{l}=\frac{125*10^{-3}*2.35*10^{-5}}{1.8}=1.6*10^{-6}\:\rm \Omega\cdot m$$