Question

calculate resistivity of material of wire 1 my long .4mm in diameter and having a resistance of 2 omega? ​

Answer 1

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The Given information is :

▶ Length of the wire (l) = 1 m

▶ diameter of the wire (d) =4mm = 4×10^-3 m

Hence, radius (r) =2×10^-3 m

▶ Resistance (R) = 2 ohm

We know that , Resistance of a conductor is directly proportional to the length of the conductor and inversely proportional to the area of cross section.

$R \: \alpha \: l \: / A$

where, R= Resistance of the conductor

l= length of the conductor

A = Area of cross section

$R = S \times \: l/A$

Here, S=Specific resistance or resistivity

The specific resistance or resistivity of the material of a conductor

$S = \: RA \: / \: l$

$S = R\times \pi \: {r}^{2} /l$

$S =2 \times 3.14 \times 4 \times {10}^{ - 6} /1$

$S =8 \times 3.14 \times {10}^{ - 6}$

$S =25.12 \times {10}^{ - 6} \: ohm \: meter$

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