Question

Derive an expression for the resistance of a metallic wire in terms of resistivity...?

Answer 1

r inverse proportional to 1/a
r directly proportional to L
combining 1 ND 2
r inverse proportional to L/A

r=Pl/a

p=rho

Answer 2

Expression for resistance of metallic wire in terms of resistivity:  $\bold{{R=\rho \frac{l}{A}}}$

Solution:

The resistance of a metallic wire in terms of the resistivity is derived as follows,

Let us assume a wire with resistance R and length L and “an cross sectional area” as A.  

“Cross sectional area” is increased the resistance of wire decreases.

$\bold{R \propto \frac{1}{A}}$

Also, when length of wire is increased the resistance of wire increases.

$\bold{R \propto l}$

Therefore, combining both the equations we get

$\begin{array}{c}{R \propto \frac{l}{A}} \\ \\{R=\rho \frac{l}{A}}\end{array}$

$\rho$– Resistivity of metallic wire.