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A heating element using nichrome connected to a 230V supply draws an initial current of 3.2A which settles after a few seconds to a steady value of 2.8A. What is the steady temperature of the heating element if the room temperature is $27.0 ° C$ ? Temperature coefficient of resistivity of nichrome averaged over the temperature range involved is $1.70 \times 10^{- 4} / C^{0}$ ?

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$840 ° C$

$871 ° C$

$1040 ° C$

$1067 ° C$

answer is B.

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Detailed Solution

$v = iR = i' R'$

$3.2 R_{0} (1 + 27 α) = 2.8 R_{0} (1 + αt)$

$8 (1 + 27 α) = 7 (1 + αt)$

$1 = α (7 t - 216) \frac{10^{4}}{1.7} = (7 t - 216) t ≅ 872^{0} C$

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