Question

The resistivity of copper is 1.6 x 10-8 Ωm. What will be the length of the wire if its radius is 1mm

and resistance is 8Ω?​

Answer 1

Answer:

the length of the wire is 184.7 meters

Explanation:

The resistance of the wire is expressed as R=

A

ρL

where,

rho is the resistivity of the wire,

L is the length of the wire,

A is the area of coss section of the wire.

It is given that the radius of the wire is 1 mm, that is 0.001 m. Therefore the area of cross section is given as πr

2

=3.14×0.001

2

=3.14×10

−6

.

Hence, the resistance of the wire when the resistance is 1 ohm, radius is 1mm, that is 0.001m and resistivity is 1.7\times { 10 }^{ -8 }\quad ohm-meter is expressed as 1=

3.14×10

−6

1.7×10

−8

×L

.

So the length L is derived as follows,

L=

1.7×10

−8

1×3.14×10

−6

=

1.7×10

−8

3.14×10

−6

=1.847×10

−2

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