Question

A given length of awire is doubled on itself and this process is repeated once again . By what factor does the resistance of the wire change ?

Answer 1

Resistance of a wire is directly proportional to the length of the wire. As its length increases it's resistance increases.

Let x be the resistance of a wire of length L

If length of a wires is doubled to 2L its resistance is doubled to 2x

If it is doubled again, the length of the wire becomes 4L and it's resistance becomes 4x.

Thus if a given length of a wire is doubled on itself and this process is repeated once again it's resistance increases by a factor of 4

Answer 2

Let the resistance of the wire be R.
Let L be the length of the wire.
When the wire is doubled , Then L will become L/2.
As length of the wire is reduced to  L/2, area increases by 2 times.

Again the process is repeated, hence L will become L/4As length of the wire reduced by L/4, area increases by 4 times.
so new reistance will be R/4
The new resistance of the wire will be effective resistance of the resistors in parallel.

1/Reff=1/R1+1/R2+1/R3+1/R4

=1/R/4+1/R/4+1/R/4+1/R/4=16/RReff=R/16Thus the resistance of the wire reduces by 16 times