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JIPMER 2016
Exam
JIPMER
Year
2016
Subject
Physics
Chapter
Current Electricity

JIPMER 2016 · Physics · Current Electricity

The length of a given cylindrical wire is increased by 150 \% . Due...

The length of a given cylindrical wire is increased by 150%150 \%. Due to the consequent decrease in diameter the change in the resistance of the wire will be

Options

  1. A200%
  2. B525%
  3. C300%
  4. D400%

Correct answer

B. 525%

Step-by-step solution

If suppose initial length, I1=100I_1=100, then I2=100+150=250∵R1R2=(I1I2)2=(100250)2⇒R1R2=425⇒R2=254R1I_2=100+150=250 \because \quad \frac{R_1}{R_2}=\left(\frac{I_1}{I_2}\right)^2=\left(\frac{100}{250}\right)^2 \Rightarrow \quad \frac{R_1}{R_2}=\frac{4}{25} \Rightarrow R_2=\frac{25}{4} R_1⇒ΔRR×100=R2−R1R1×100=254R1−R1R1×100=525%\begin{aligned} \Rightarrow \frac{\Delta R}{R} \times 100 & =\frac{R_2-R_1}{R_1} \times 100 \\ & =\frac{\frac{25}{4} R_1-R_1}{R_1} \times 100=525 \%\end{aligned}$$
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