A conducting wire has a resistance R. It is stretched to double its initial length. Calculate its newresistance in terms of R
Question
A conducting wire has a resistance R. It is stretched to double its initial length. Calculate its newresistance in terms of R
Solution
The resistance (R) of a wire is given by the formula R = ρL/A, where ρ is the resistivity, L is the length, and A is the cross-sectional area.
When the wire is stretched to double its initial length, the volume of the wire remains constant. So, the new length (2L) and the new cross-sectional area (A/2) are inversely proportional.
Substituting these values into the resistance formula gives the new resistance (R') as R' = ρ(2L)/(A/2).
Simplifying this gives R' = 4ρL/A.
Since the initial resistance R = ρL/A, we can substitute this into the equation for R' to give R' = 4R.
So, when the wire is stretched to double its initial length, its resistance increases by a factor of 4.
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