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?
Dear Student,
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- Let the initial length of the wire be x,area be A and resistance be R.
- As the resistance of the wire is directly proportional to its length And inversely to area.
- Then the length of the wire is doubled(folded) so the length becomes x/2,area 2A and Resistance R/4 and again the process is repeated so the length becomes x/4,area 4A and Resistance R/16.
- So the resistance change by the factor of 1/16.
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