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26 July, 22:59

An electric heater has a Nichrome heating element with a resistance of 9 Ω at 20oC. When 112 V are applied, the electric current heats the Nichrome wire to 1090oC. What is the operating wattage of this heater? (The temperature coefficient of resistivity of Nichrome is α = 0.0004 Co-1)

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  1. 27 July, 01:40
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    975.28 W.

    Explanation:

    Using,

    R' = R (1+αΔt) ... Equation 1

    Where R' = Resistance at the final temperature, R = Resistance at the initial temperature, α = temperature coefficient of resistivity of Nichorome, Δt = Temperature rise.

    Given: R = 9 Ω, α = 0.0004/°C, Δt = 1090-20 = 1070 °C

    Substitute into equation 1

    R' = 9 (1+0.0004*1070)

    R' = 9 (1.428)

    R' = 12.862 Ω.

    Note: Operating wattage of the heater means the operating power of the heater

    The power of the heater is given as,

    P = V²/R' ... Equation 2

    Where P = Operating wattage of the heater, V = Voltage, R' = Operating resistance.

    Given: V = 112 V, R' = 12.862 Ω

    Substitute into equation 2

    P = 112²/12.862

    P = 975.28 W.
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