Question

If $n$ , $e$ , $\tau$ and $m$ represent electron density, charge, relaxation time and mass of an electron respectively, then the resistance of a wire of length $l$ and cross-sectional area $A$ is

• A. $\frac{ml}{ne^{2} τA}$
• B. $\frac{mτA}{ne^{2} l}$
• C. $\frac{ne^{2} τA}{ml}$
• D. $\frac{ne^{2} ml}{τA}$

Answer 1

Answer: (A)

$R=\rho \frac{l}{A}$
Since we know resistivity is given by $\rho =\frac{m}{ne^{2} r}$
Resistance $R=\frac{ml}{ne^{2} τA}$
where,
$m=$ Mass of electron
$l=$ length of conductor
$n=$ charge density
$\text{e}=$ charge of electron
$\tau=$ relaxation time
$A=$ cross-sectional area