Question

You are working in lab was given a task by your supervisor to determine the density of a material which he wanted use in a circuit. Material he gave was a very skinny wire with a mass of 0.001 kg, length of 2.4 x 103 m long and having a resistance of 2.71 x 106 Ώ. Knowing the resistivity of the material as 2.44 x 10-8 Ώ.m, determine the density of the material.

Answer 1

Sol::
Given

Mass (m) = 0.001 kg,
length(l)= 2.4 x 10^3 m
Resistance(R)= 2.71 x 10^6 Ω
Resistivity (ρ)=2.44 x 10^-8 Ω m

We know that

Resistance R= ρl/A

So

A= ρL/R
= (2.44 x 10^-8)(2.4 x 10^3)/(2.71 x 10^6)
= 2160.88*10^-11 m²
≈ 2.16*10^-11m²

Now
Mass = volume*density
So
Density (d) = m/V
= m/AL
= 0.001/(2.16*10^-11)(2.4 x 10^3)
= 0.001/5.184*10^-8
= 0.0001929*10^8
≈ 1.93*10^4 kg/m³

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