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Question

A heating element using nichrome connected to a 230 V supply draws an initial current of 3.2 A which settles after a few seconds to a steady value of 2.8 A. What is the steady temperature of the heating element if the room temperature is 27.0 °C ?Temperature coefficient of resistance of nichrome averaged over the temperature range involved is 1.70 × 10-4°C-1.

A 827°C Correct Answer Incorrect Answer
B 877°C Correct Answer Incorrect Answer
C 857°C Correct Answer Incorrect Answer
D 867°C Correct Answer Incorrect Answer

Solution

At room temperature 27°C, the resistance of the heating element. R27° = 230/3.2 = 71.875 ohm At the steady temperature t° C, the resistance Rt = 280/2.8 = 82.143 ohm Now, R2 = R1[1 + α(t2 - t1) => 82.143 = 71.875[1 + 1.7 x 10-4(t - 27)] => 0.0840 x 104 = t - 27 => 840 = t - 27 => t = 867°C

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