Q152 / 160 · TS EAMCET 2007 · Physics

An aluminium (resistivity $\rho=2.2 \times 10^{-8} \Omega$-m) wire of a diameter $1.4 \mathrm{~mm}$ is used to make a $4 \Omega$ resistor. The length of the wire is

  • A
    $220 \mathrm{~m}$
  • B
    $1000 \mathrm{~m}$
  • Correct answer
    C
    $280 \mathrm{~m}$
  • D
    $1 \mathrm{~m}$

Solution

Length of the wire is $\begin{array}{rl}\quad l & =\frac{R A}{\rho} \\ \therefore \quad l & l \\ \therefore \quad & \frac{4 \times \pi \times\left(0.7 \times 10^{-3}\right)^2}{2.2 \times 10^{-8}} \\ & =280 \mathrm{~m}\end{array}$

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

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