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Current Electricity

Question
CBSEENPH12040050

A wire of a certain material is stretched slowly by ten percent. Its new resistance and specific resistance become respectively

  • 1.2 times, 1.1 times

  • 1.21 times, same

  • both remain the same

  • 1.1 times, 1.1 times

Solution

B.

1.21 times, same

In stretching, specific resistance remains unchanged.
After stretching, specific resistance (rho) will remain same.
Original resistance of the wire,
straight R space equals space ρl over straight A
or
straight R proportional to space straight l over straight A space or space space space straight R proportional to straight l squared over straight V space left parenthesis as space straight V equals Al right parenthesis
and space straight R apostrophe space proportional to space fraction numerator left parenthesis 1 plus 10 percent sign straight l right parenthesis squared over denominator straight V end fraction
therefore comma space fraction numerator straight R apostrophe over denominator straight R end fraction space equals space open parentheses straight l plus begin display style 10 over 100 end style straight l close parentheses squared over straight l squared
or space fraction numerator straight R apostrophe over denominator straight R end fraction space equals open parentheses fraction numerator 11 space straight l over denominator 10 end fraction close parentheses squared space equals space 121 over 100
or space straight R apostrophe space equals space 1.21 space straight R

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