Question

A given wire of resistance 10Ω has a length of 5m and a cross sectional area of 4.0×10^-3m^2, Calculate the conductivity of the wire

Answer 1

Let's first find the resistivity of the wire from the formula:

$$\rho =R \dfrac{A}{l},$$

here, $R = 10 \Omega$ is the resistance of the wire, $A = 4.0 \cdot 10^{-3} m^2$ is the cross-sectional area of the wire and $l = 5 m$ is the length of the wire.

Then, we get:

$$\rho = 10 \Omega \cdot \dfrac{4.0 \cdot 10^{-3} m^2}{5m} = 8.0 \cdot 10^{-3} \Omega \cdot m.$$

Finally, we can find the conductivity of the wire from the formula:

$$\sigma = \dfrac{1}{\rho} = \dfrac{1}{8.0 \cdot 10^{-3} \Omega \cdot m} = 125 \dfrac{S}{m}.$$

Answer:

$\sigma = 125 \dfrac{S}{m}.$