Question

The resistivity of manganese wire of length 1m is 1.84×10^-6 ohm metre at 20 degree Celsius. If the diameter of the wire is 3× 10^-4 metre, what will be the resistance of the wire at that temperature?​

Answer 1

resistivity = 1.84×10^-6 ohm metre

length = 1m

Diameter = 3×10^-4 metre

Resistance=?

A=πr^2

Answer 2

Given:

Resistivity of manganese at 20°C, , ρ$=1.84*10^{-6}$Ωm

Length of the wire, $l=1m$

Diameter of the wire, $d=3*10^{-4}m$

To FInd:

Resistance of the wire at that temperature, $R=?$

Solution:

We know that the resistance of a wire, having a resistivity ρ, cross-sectional area $A$ and length $l$ is, $R=$ρ*$\frac{l}{A}$

                                                  ∴ $R=$ ρ$*\frac{l}{\pi (d/2)^2}$

                                                         $=$ ρ$*\frac{4l}{\pi d^2}$

                                                         $=\frac{4*1.84*10^{-6}}{3.14*(3*10^{-4})^2}$

                                                         $=26.04$Ω.

Hence, the resistance of the wire, R=26.04Ω.