Question:
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 change?
Answer:
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.
Thus, 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
Thus, the resistance of the wire reduces by 16 times.
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