Question

a given wire is doubled on itself twice by what factor does the resistence of wire change ?

Answer 1

Let the resistance of the wire be R.

When the wire is doubled on itself and the process is repeated then - 

The length of the wire reduces by 1/2, and the area increases by 2 times. 

this giving us the resistance of the wire reduced by 1/4 times.

So, resistance = R/4

So, the total resistance of the wire when the resistors are arranged in parallel,

1/Rp = 1/(R/4) + 1/(R/4) + 1/(R/4) + 1/(R/4)

Rp = R/16