Answer:
\(r=\frac{\rho}{A}\)
Step-by-step explanation:
Given,
Resistance (r) in a wire increases when the length of the wire (l) increases,
That is, r is proportional to l
\(r\propto l\)
Also, we know that Resistance is inversely proportional to the cross sectional area, A,
That is,
\(r\propto \frac{1}{A}\)
By combining,
\(r\propto \frac{l}{A}\)
\(r=\rho \frac{l}{A}\)
Where, \(\rho\) is the resistivity constant.
Given, l = 1 unit,
Hence, the required formula would be,
\(r=\frac{\rho}{A}\)
