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BITSAT 2024
Exam
BITSAT
Year
2024
Subject
Physics
Chapter
Current Electricity

BITSAT 2024 · Physics · Current Electricity

A conducting wire is stretched by applying a deforming force, so...

A conducting wire is stretched by applying a deforming force, so that its diameter decreases to 40%40 \% of original value. The percentage change in its resistance will be

Options

  1. A0.9%0.9 \%
  2. B0.12%0.12 \%
  3. C1.6%1.6 \%
  4. D0.5%0.5 \%

Correct answer

C. 1.6%1.6 \%

Step-by-step solution

On stretching, volume of wire remains constant. So, V=AlV=A l or l=VAl=\frac{V}{A}∴R=ρ⋅lA=ρVA2=ρVπ2D416=16ρVπ2D4∴ΔRR=−4ΔDD=−4(−0.4)=1.6%\begin{array}{ll} \therefore & R=\rho \cdot \frac{l}{A}=\frac{\rho V}{A^2}=\frac{\rho V}{\frac{\pi^2 D^4}{16}}=\frac{16 \rho V}{\pi^2 D^4} \\ \therefore & \frac{\Delta R}{R}=-4 \frac{\Delta D}{D}=-4(-0.4)=1.6 \% \end{array}$$
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