Question

Find the ratio of the diameter of aluminium to copper wire, if they have the same

resistance per unit length. Take the resistivity values of aluminium and copper to

be 2.65× 10−8 Ω m and 1.72 × 10−8 Ω m respectively​

Answer 1

1.24

Step-by-step explanation:

The resistivity of copper
`\rho_1=2.65* 10^(-8)\ \Omega-m`

The resistivity of Aluminum,
`\rho_2=1.72* 10^(-8)\ \Omega-m`

The wires have same resistance per unit length.

The resistance of a wire is given by :

`R=\rho (l)/(A)\\\\R=\rho (l)/(\pi ((d)/(2))^2)\\\\(R)/(l)=\rho (1)/(\pi ((d)/(2))^2)`

According to given condition,

`\rho_1 (1)/(\pi ((d_1)/(2))^2)=\rho_2 (1)/(\pi ((d_2)/(2))^2)\\\\\rho_1 \frac{1}{{d_1}^2}=\rho_2 \frac{1}{{d_2}^2}\\\\((d_2)/(d_1))^2=(\rho_1)/(\rho_2)\\\\(d_2)/(d_1)=\sqrt{(\rho_1)/(\rho_2)}\\\\(d_2)/(d_1)=\sqrt{(2.65* 10^(-8))/(1.72* 10^(-8))}\\\\=1.24`

So, the required ratio of the diameter of Aluminum to Copper wire is 1.24.