A thermometer is made using a carbon resistor having a temperature coefficient of resistivity of -0.00050Ω° $C^{- 1}$ .the variation of resistance with temperature in the linear reason is used to measure the temperature. On a cold winter day when the temperature is 8°C,the resistance is 216.8Ω. what is the temperature on a summer day when the resistance is 213.5Ω?

Question

A thermometer is made using a carbon resistor having a temperature coefficient of resistivity  of -0.00050Ω° $C^{- 1}$ .the variation of resistance with temperature in the linear reason is used to measure the temperature. On a cold winter day when the temperature is 8°C,the resistance is 216.8Ω. what is the temperature on a summer day when the resistance is 213.5Ω?

Accepted Answer

ঘ. 38.4°C

ব্যাখ্যা: রোধের তাপমাত্রিক সম্পর্কের রৈখিক সমীকরণ: $R_2 = R_1 [1 + \alpha(T_2 - T_1)]$ বা $T_2 - T_1 = \frac{R_2 - R_1}{\alpha R_1}$। এখানে, $T_1 = 8^\circ	ext{C}$, $R_1 = 216.8\ \Omega$, $R_2 = 213.5\ \Omega$ এবং $\alpha = -0.00050\ ^\circ	ext{C}^{-1}$। মান বসিয়ে পাই, $T_2 - 8 = \frac{213.5 - 216.8}{-0.00050 	imes 216.8} = \frac{-3.3}{-0.1084} \approx 30.44^\circ	ext{C}$। অতএব, $T_2 = 8 + 30.44 = 38.44^\circ	ext{C} \approx 38.4^\circ	ext{C}$।

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