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 new resistance 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, its volume remains constant. The volume of the wire can be given as V = AL, so when the length is doubled, the cross-sectional area is halved.
The new resistance (R') of the wire can be calculated using the same formula, but with the new length (2L) and new cross-sectional area (A/2).
So, R' = ρ(2L)/(A/2) = 4ρL/A = 4R.
Therefore, the new resistance of the wire is four times its original resistance.
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