Question

A 20 meter length of cable has a cross-sectional area of 1mm2 and a resistance of 5 ohms. Calculate the conductivity of the cable. 𝜎 = 4𝑥106𝑠𝑖𝑒𝑚𝑒𝑛𝑠

What will be the conductivity of the cable if its length is (a) reduced by 1⁄4 of its original length (b) doubled?

Answer 1

Let's first find the resistivity of the cable:

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

Finally, we can calculate the conductivity of the cable:

$$\sigma=\dfrac{1}{\rho}=\dfrac{l}{RA}=\dfrac{20\ m}{5\ \Omega\cdot1\ mm^2\cdot(\dfrac{1\ m}{1000\ mm})^2}=4\cdot10^6\ \dfrac{S}{m}.$$

a)

$$\sigma_{new}=\dfrac{l}{4RA}=\dfrac{1}{4}\cdot\sigma=\dfrac{1}{4}\cdot4\cdot10^6\ \dfrac{S}{m}=10^6\ \dfrac{S}{m}.$$

(b)

$$\sigma_{new}=\dfrac{2l}{RA}=2\sigma=2\cdot4\cdot10^6\ \dfrac{S}{m}=8\cdot10^6\ \dfrac{S}{m}.$$