A resistor made of Nichrome wire is used in an application where its resistance cannot change more than 1.30% from its value at 20.0°C. Over

Question

A resistor made of Nichrome wire is used in an application where its resistance cannot change more than 1.30% from its value at 20.0°C. Over what temperature range can it be used (in °C)?

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Hải Đăng 3 years 2021-08-02T14:43:23+00:00 1 Answers 28 views 0

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  1. thaiduong
    0
    2021-08-02T14:44:36+00:00
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    Answer:

    – 12.5 °C to 52.5 °C

    Explanation:

    Let the initial resistance is Ro and the initial temperature is To = 20°C.

    temperature coefficient of resistance, α = 0.0004 /°C

    Case I : For maximum resistance:

    Maximum resistance, R’ = Ro + 1.30 % of Ro

    R' = R_{0}\left ( 1+\frac{1.3}{100} \right )=1.013 R_{0}

    let the temperature difference is ΔT.

    R’ = Ro (1 + αΔT)

    1.013 Ro = Ro ( 1 + 0.0004 ΔT)

    ΔT = 32.5 °C

    So, the maximum value of resistance is

    T = 32.5 + 20 = 52.5 °C

    Case II: For minimum value of resistance :

    Minimum resistance, R” = Ro – 1.30 % of Ro

    R'' = R_{0}\left ( 1-\frac{1.3}{100} \right )=0.987 R_{0}

    let the temperature difference is ΔT.

    R” = Ro (1 + αΔT’)

    0.987 Ro = Ro ( 1 + 0.0004 ΔT’)

    ΔT’ = – 32.5 °C

    So, the maximum value of resistance is

    T’ = – 32.5 + 20 = – 12.5 °C

    So, the range of temperature is – 12.5 °C to 52.5 °C.

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