Question

A copper wire is 1 metre long and has a uniform cross section of 0.1 mm2. The resistance of the wire at room temperature is 0.171 ohm. What is the resistivity of the material? (a) 1.71 x 10-6 2.m. (b) 1.71 x 10-7 2.m. (c) 1.71 x 10-8 2.m. (d) 1.71 x 10-92.m. ​

Answer 1

Given,

l=0.1m=1000mm

d=0.2mm∴radius(r)=

2

0.2

=0.1mm

R=10Ω

To find,

Resistivity(ρ)

ρ=R

l

A

where,

R= Resistance

l= Length of wire

A= Cross sectional area of wire

Cross sectional area of cylinder (A)=Πr

2

⇒A=π×(0.1)

2

⇒A=0.0314mm

2

∴ρ=10(

1000

0.0341

)

⇒ρ=0.000314Ω−mm

⇒ρ≃3.14×10

−7

Ω−m

So, the resistivity of the material is equal to 3.14×10

−7

Ω−m