A given length of a wire is doubled on itself and this process is repeated once again.

By what factor does the resistance of the wire changes ?

I take the wire is doubled back on itself instead of doubled on itself.

 Let this be the wire

It is doubled back  

Process is again repeated so it results

(Wires touch each other at the ends)

Let the original wire have a resistance = R

Resistance of each wire of L/4 length = R/4

So this becomes parallel combination of four resistors

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

=> Rp = R/16

So the resistance of the wire changes by a factor of 1/16 


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