Q42 / 50 · Manipal (MET) 2023 · Physics

The resistance of a wire at $20^{\circ} \mathrm{C}$ is $20 \Omega$ and at $500^{\circ} \mathrm{C}$ is $60 \Omega$. At which temperature its resistance will be $25 \Omega$ ?

  • A
    $50^{\circ} \mathrm{C}$
  • B
    $60^{\circ} \mathrm{C}$
  • C
    $70^{\circ} \mathrm{C}$
  • Correct answer
    D
    $80^{\circ} \mathrm{C}$

Solution

Resistance, $R_t=R_0(1+\alpha t)$ $20=R_0(1+20 \alpha) \text { and } 60=R_0(1+500 \alpha)$ From this equation, we can find $\begin{aligned} R_0 & =18.33 \Omega \\ \alpha & =4.54 \times 10^{-3} \\ R_t & =25 \Omega\end{aligned}$ $\begin{aligned}& \text { Again, } \quad R_t=R_0(1+\alpha t) \\ & 25=18.33\left(1+4.54 \times 10^{-3} t\right)\end{aligned}$ $\text { We find } t=80^{\circ} \mathrm{C}$

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

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