A solid metal cylinder has a certain resistance. It is then heated and carefully

Question

A solid metal cylinder has a certain resistance. It is then heated and carefully stretched to form a longer, thinner cylinder. After it cools, will its resistance be the same as, greater than, or less than what it was before?

a. The resistance will be the same since the resistance is independent of the length and cross-sectional area. Increasing the length and shrinking the radius will not affect the resistance.

b. The resistance will be greater since the resistance is proportional to length and inversely proportional to cross-sectional area. Increasing the length and shrinking the radius both act to increase the resistance.    

c. The resistance will be less than before since the resistance is inversely proportional to length and proportional to cross-sectional area. Increasing the length and shrinking the radius both act to decrease the resistance.

Explanation / Answer

As, Resistance = (rho * L)/A

where, rho = resistivity

           L = length

           A = cross sectional area

=> Correct answer is :

b . The resistance will be greater since the resistance is proportional to length and inversely proportional to cross-sectional area. Increasing the length and shrinking the radius both act to increase the resistance.    

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