Question

A cylindrical conductor of length 'l' and uniform area of cross - section 'A' has resistance 'R' . Another conductor of length 2.5 l and resistance 0.5 R of the same material has area of cross - section .
Explain your answer .

Answer 1

Dear Student,
Given,
Cylindrical conductor, say A:
Length = l
Area of cross-section = A
Resistance = R
Another Cylindrical conductor, say B:
Length, l' = 2.5l
Resistance, R' = 0.5 R
Let its are of cross-section be A'
Let the resistivity of the material of A and B be $\rho$
Then,
$$\begin{gathered} \rho =\frac{RA}{l}=\frac{R\text{'}A\text{'}}{l\text{'}} \\ \frac{RA}{l}=\frac{0.5RA\text{'}}{2.5l} \\ \therefore A\text{'}=5A \end{gathered}$$

Regards