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Question: Answered & Verified by Expert
The resistance of a wire is $5 \Omega$. It's new resistance in ohm if stretched to 5 times of its original length will be :
PhysicsCurrent ElectricityBITSATBITSAT 2023 (Memory Based Paper 1)
Options:
  • A 625
  • B 5
  • C 125
  • D 25
Solution:
3000 Upvotes Verified Answer
The correct answer is: 125



Let resistance of a wire $R$ and length 1 .
$\mathrm{R}=\frac{\rho \ell}{\mathrm{A}}=5 \Omega$
$\therefore \quad$ Volume of wire is constant in stretching
$V_i=V_f \Rightarrow A_i \ell_i=A_f \ell_f$
$\mathrm{A} \ell=\mathrm{A}^{\prime}(5 \ell) \Rightarrow \mathrm{A}^{\prime}=\frac{\mathrm{A}}{5}$
$R_f=\frac{\rho \ell_f}{A_f}=\frac{\rho(5 \ell)}{\left(\frac{A}{5}\right)}=25\left(\frac{\rho \ell}{A}\right)=25 \times 5=125 \Omega$

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