Question

2. What length of copper wire of specific resistance
1-7 x 10-8 22 m and radius 1 mm is required so that
its resistance is 192 ?
Ans. 184.7 m​

Answer 1

Explanation:

he resistance of the wire is expressed as R=AρLwhere,

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 πr2=3.14×0.0012=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=3.14×10−61.7×10−8×L.

So the length L is derived as follows,

L=1.7×10−81×3.14×10−6=1.7×10−83.14×10−6=1.847×10−2.

Hence, the length of the wire is 184.7 meters.