Question

A wire of length 3 m and area of cross-section 1.7X10-6 m2 has a resistance 3X10-2ohm.
a) What is the formula for resistivity of the wire and what is the unit of it
b) Calculate the resistivity of the wire

Answer 1

Given:

Length, L = 3 m  

Area of cross section, $A=1.7 \times 10^{-6} \ m^{2}$

Resistance, $R=3 \times 10^{-2} \ \text{ohm}$

Solution:

We have to write the formula for resistivity of wire and mention its unit and have to calculate the resistivity of the wire

a) $R=\frac{\rho L}{A}$

Where,

$\rho$ is resistivity

So,

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

The unit is ohm meter.

b) To find the resistivity of the wire use the above formula and substitute the given values in the formula

Hence, we get,

$\rho=\frac{\left(3 \times 10^{-2} \times 1.7 \times 10^{-6}\right)}{3}$

Hence, the resistivity,

$\rho=1.7 \times 10^{-8} \ \text { ohm } m$

Answer 2

Formula for Resistivity of Wire is $\bold{\rho=\frac{R \times A}{l}}$

Unit of Resistivity is ohm meter.

Resistivity of wire is $\bold{1.7 \times 10^{-8} \text { ohm } m}$  

Solution:

The formula for resistivity of a given wire is derived from the formula of resistance of the wire, which is as follows,

$\begin{array}{l}{\boldsymbol{R}=\boldsymbol{\rho} \frac{\boldsymbol{l}}{\boldsymbol{A}}} \\ \\{\boldsymbol{\rho}=\frac{\boldsymbol{R} \times \boldsymbol{A}}{l}}\end{array}$

Now for unit of resistivity of the given wire, as known from the formula, we have  

$\begin{aligned} \rho &=\frac{o h m \times m e t e r^{2}}{m e t e r} \\ \rho &=o h m \times \text { meter } \\ \rho &=\text { ohm meter } \end{aligned}$

Now as calculate resistivity of the given wire, we have –

$\begin{array}{l}{R=3 \times 10^{-2} \text { ohm }} \\ {A=1.7 \times 10^{-6} \mathrm{m}^{2}} \\ {l=3\ \mathrm{m}}\end{array}$

$\begin{array}{l}{\rho=\frac{3 \times 10^{-2} \times 1.7 \times 10^{-6}}{3}} \\ {\rho=1.7 \times 10^{-8} \text { ohm } m}\end{array}$