Question

2.A copper wire has diameter 1 mm and resistivity of 1.6 × 10 –8 Ω m. What will be

the length of this wire to make its resistance 10 Ω? How much does the resistance

change if the diameter is doubled?​

Answer 1

Answer:

Explanation:Given, diameter, d=0.5 mm

           resistivity, ρ=1.6×10  

−8

 Ωm

           Resistance, R=10 Ω

Let the length of wire be l.

    A=πd  

2

/4

    R=ρl/A

             =  

πd  

2

/4

ρl

​  

 

⟹l=  

4ρ

Rπd  

2

 

​  

 

            l=  

4×1.6×10  

−8

 

10×3.14×(0.5×10  

−3

)  

2

 

​  

 

            l=122 m

        R∝1/d  

2

 

If the diameter is doubled, resistance will be one-fourth.

Hence, new resistance =2.5Ω