a 6cm long wire has diameter 0.5mm.its resistance is 50 om ga.find the resistivity qand conductivity of wire
Answers
Answer:
Answer:
1.63\times 10^{-4}1.63×10−4 and 6.11\times 10^{-4}6.11×10−4
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= 0.5×10−3 m
Radius of wire,
r\ =\ \dfrac{diameter}{2}r = 2diameter
=\ 2.5\times 10^{-3}= 2.5×10−3
Area of cross-section of wire,
a\ =\ \pi\times r^2a = π×r2
=\ \pi\times (2.5\times 10^{-3})^2= π×(2.5×10−3)2
=\ 19.625\times 10^{-6}\ m^2= 19.625×10−6 m2
Now, resistivity of the wire is ,
\rho\ =\ \dfrac{R.a}{l}ρ = lR.a
=\ \dfrac{50\times 19.625\times 10^{-6}}{6}= 650×19.625×10−6
=\ 1.63\times 10^{-4}\ ohm-m= 1.63×10−4 ohm−m
\textrm{now,\ conductivity\ }=\ \dfrac{1}{resistivity}now, conductivity = resistivity1
=\ \dfrac{1}{1.63\times 10^{-4}}\ \mho= 1.63×10−41 ℧
=\ 6.11\times 10^{-4}\ \mho-m^{-1}= 6.11×10−4 ℧−m−1
Hence, the resistivity of the wire is 1.63\times 10^{-4}\ ohm-m1.63×10−4 ohm−m and conductivity is 6.11\times 10^{-4}\ \mho-m^{-1}.6.11×10−4 ℧−m−1.