Q118 / 180 · NEET 2013 (All India) · Physics

A wire of resistance $4 \Omega$ is stretched to twice its original length. The resistance of stretched wire would be

  • A
    $2 \Omega$
  • B
    $4 \Omega$
  • C
    $8 \Omega$
  • Correct answer
    D
    $16 \Omega$

Solution

Let length and cross-section area of the wire be l and A respectively. \(\therefore\) Resistance \(\mathrm{R}=\rho \frac{\mathrm{l}}{\mathrm{A}}\) where \(\rho\) is the resistivity of the material Given: \(R=4 \Omega\) For \(l^{\prime}=2 l\) and \(A^{\prime}=\frac{A}{2}\), resistance of the wire be \(R^{\prime}\) \(\begin{aligned} & \therefore R^{\prime}=\rho \frac{l^{\prime}}{A^{\prime}}=\rho \frac{2 l}{A / 2}=4 \rho \frac{1}{A}=4 R \\ & \therefore R^{\prime}=4 \times 4 \Omega=16 \Omega \end{aligned}\)

Hence, the correct answer is option: 'D'.

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