Question

Which among the following equation gives the correct relation between resistance $\left(R\right)$, length of conductor $\left(L\right)$, area of the cross-section of the conductor $\left(A\right)$ and resistivity$\left(\rho \right)$?

• 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

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

Resistance of the conductor depends on,
(i) its length, and
(ii) its area of cross-section.
Measurements have shown that resistance of a conductor is directly proportional to its length $\left(L\right)$ and inversely proportional to the area of cross-section $\left(A\right)$.
i.e $R\alpha L$ and $R\propto \frac{1}{A}$
$\Rightarrow R\alpha \frac{L}{A}$
or $R=\rho \times \frac{L}{A}$, where $\rho$ is the proportionality constant, i.e. resistivity.