Q191 / 200 · Manipal (MET) 2011 · Physics

At what temperature will the resistance of a copper wire become three times its value at $0^{\circ} \mathrm{C}$ ? (temperature coefficient of resistance for copper $=4 \times 10^{-3} /{ }^{\circ} \mathrm{C}$ )

  • A
    $400^{\circ} \mathrm{C}$
  • B
    $450^{\circ} \mathrm{C}$
  • Correct answer
    C
    $500^{\circ} \mathrm{C}$
  • D
    $550^{\circ} \mathrm{C}$

Solution

From definition of temperature resistance coefficient $\begin{aligned} R_t & =R_0(1+\alpha t) \\ 3 R_0 & =R_0\left(1+4 \times 10^{-3} t\right) \\ 3 & --1+4 \times 10^{-3} t \\ 4 & \times 10^{-3} t=2 \\ t & =\frac{2}{4 \times 10^{-3}} \\ & =500^{\circ} \mathrm{C}\end{aligned}$

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

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