The nichrome heating element of a toaster has a resistance at 12Ω when it's red hot (1200°C). What's the resistance of the element at room temperature (27°C)? [temperature coefficient of resistance of nichrome is 0.4×10-3 °C-1]

Question

The nichrome heating element of a toaster has a resistance at 12Ω when it's red hot (1200°C). What's the resistance of the element at room temperature (27°C)? [temperature coefficient of resistance of nichrome is 0.4×10-3 °C-1]

Accepted Answer

ক. 8.167Ω

ব্যাখ্যা: তাপমাত্রার সাথে রোধের পরিবর্তনের সূত্রানুসারে, $R_T = R_0 (1 + \alpha \Delta T)$। এখানে $T_1 = 27^\circ	ext{C}$ তাপমাত্রার রোধ $R_{27}$ এবং $T_2 = 1200^\circ	ext{C}$ তাপমাত্রায় রোধ $R_{1200} = 12\,\Omega$। অতএব, $\Delta T = 1200 - 27 = 1173^\circ	ext{C}$। সুতরাং, $R_{1200} = R_{27} [1 + \alpha \Delta T] \implies 12 = R_{27} [1 + 0.4 	imes 10^{-3} 	imes 1173] = R_{27} [1 + 0.4692] = 1.4692 R_{27}$। ফলে $R_{27} = \frac{12}{1.4692} \approx 8.167\,\Omega$।

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