Question

A 6 m long wire has diameter of 0.5 mm its resistance is 50 ohms find the Resistivity and conductivity

Answer 1

Answer:

resistivity=1.636×10^(-6) ohm m, conductivity=0.611×10^(6)

Explanation:

resistivity=(RA) ÷l

conductivity=1÷resistivity

Answer 2

Answer:

$1.63\times 10^{-4}$ and $6.11\times 10^{-4}$

Explanation:

Given,

Resistance of wire, R = 50 ohms

Length of wire,l = 6m

Diameter of wire, d= 0.5 mm

                              $=\ 0.5\times 10^{-3}\ m$

Radius of wire,

                $r\ =\ \dfrac{diameter}{2}$

                  $=\ 2.5\times 10^{-3}$

Area of cross-section of wire,

                     $a\ =\ \pi\times r^2$

                          $=\ \pi\times (2.5\times 10^{-3})^2$

                         $=\ 19.625\times 10^{-6}\ m^2$

Now, resistivity of the wire is ,

                              $\rho\ =\ \dfrac{R.a}{l}$

                                       $=\ \dfrac{50\times 19.625\times 10^{-6}}{6}$

                                         $=\ 1.63\times 10^{-4}\ ohm-m$

$\textrm{now,\ conductivity\ }=\ \dfrac{1}{resistivity}$

                              $=\ \dfrac{1}{1.63\times 10^{-4}}\ \mho$

                              $=\ 6.11\times 10^{-4}\ \mho-m^{-1}$

Hence, the resistivity of the wire is $1.63\times 10^{-4}\ ohm-m$ and conductivity is $6.11\times 10^{-4}\ \mho-m^{-1}.$