Question

A copper wire of length $4.5m$ and area of cross-section $1.7\times {10}^{-5}{m}^2$ has a resistance of $4.5\times {10}^{-2}ohms$. Calculate the resistivity of copper.

Answer 1

Given: A copper wire of length $4.5m$ and area of cross-section $1.7\times {10}^{-5}{m}^2$ has a resistance of $4.5\times {10}^{-2}\Omega$

To Find the resistivity of copper.

Solution:

Let $R=4.5\times {10}^{-2}\Omega$ be resistance, $A=1.7\times {10}^{-5}{m}^2$ be the area of cross section of wire, $L=4.5m$ be length of given wire and $\rho$ be the coefficient of resistivity.

We know,

$R=\rho \frac{l}{A}⟹4.5\times {10}^{-2}=\rho \frac{4.5}{1.7\times {10}^{-5}}⟹\rho =1.7\times {10}^{-5-2}⟹\rho =1.7\times {10}^{-7}\Omega m$

is the required resistivity of the copper.