Question

The specific resistance of copper at 0˚C is 1.72X10-8 - m. What should be the length

of copper wire having diameter =0.0002 m to have a resistance of 5 Ω at 0 ˚C?​

Answer 1

Answer:

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

.

Hence, the length of the wire is 184.7 meters.