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25 December, 10:36

A Nichrome wire is used as a heating element in a toaster. From the moment the toaster is first turned on to the moment the wire reaches it maximum temperature, the current in the wire drops by 20% from its initial value. What is the temperature change in the wire? The temperature coefficient for Nichrome is α = 0.0004 (°C) - 1.

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  1. 25 December, 11:04
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    Temperature change in the wire is 625°C

    Explanation:

    Let the initial current in the wire be I₀

    Thus,

    the final current in the wire will be, I = (1 - 0.20) * I₀ = 0.80I₀

    Given α = 0.0004 1/°C

    Now,

    Resistance = (potential difference (E)) / current (I)

    also

    R = R₀ [1 + αΔT]

    Where ΔT is the increase in temperature, thus

    E/I = E/I₀ [1 + α * ΔT)

    on substituting the values in the above equation, we get

    1 / (0.80I₀) = 1 / (I₀) * [1 + 0.0004 * ΔT]

    or

    1 / (0.80) = [1 + 0.0004 * ΔT) ]

    or

    ΔT = 625°C
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