Question

if the area of a conducting wire increased by 2 times and length of a conducting is reduced to half. then what will be resistance?

Answer 1

Let the original length of the wire = l meters
Also, let the area of the wire = a m²
Resistance-1 = ρ length/area
                      = ρ l/a

Now, the cross-sectional area increased by 2 times and the length reduced to half .
Cross-sectional area = 2a m²
length  = l/2 m
Resistance -2 = ρ (l/2)/2a
Resistance -2 = ρ l/2 * 1/2a
                        = ρ l/4a

The new resistance decreased by 4 times.

Hope this helps you.