Question

Which among the following equations give the correct relation between resistance(R), length of the conductor(L) and area of cross-section of the conductor(A)?

• A. $R=\frac{L}{A\times \rho }$
• B. $R=\frac{A\times \rho }{L}$
• C. $R=\frac{A\times L}{\rho }$
• D. $R=\frac{\rho \times L}{A}$

Answer 1

The correct option is D

$R=\frac{\rho \times L}{A}$

The resistance of the conductor depends on,
(i) its length,
(ii) its area of cross-section, and
(iii) the nature of its material.
Measurements have shown that resistance of a uniform metallic conductor is directly proportional to its length (L) and inversely proportional to the area of cross-section (A).
$R\alpha L$
$R\propto \frac{L}{A}$
$\Rightarrow R=\rho \times \frac{L}{A}$ where $\rho$ is the resistivity of the conductor.
Here, $\rho$ is the constant of proportionality