Question

How does the resistance of a wire change when:

 its diameter is tripled? 

 

Answer 1

Resistance, 

`R=l/A`

where l = length of  wire
            A= area of cross-section of the wire 

When the diameter is tripled, d' = 3d Radius, r' = 3r

Area of cross-section, `A=Api^2=A(3pi)^2=9Api^2=9A`

Thus, the area of cross-section will become nine times. 

Then the new resistance, 

`R'=l/A` 

`R'=l/9A` 

`R'=R/9` 

Thus, the resistance will be reduced by nine times.