A small bulb is rated at 7.5 W when operated at 125 V. The tungsten filament has a temperature coefficient of resistivity α = 0.0045/°C. Whe

Question

A small bulb is rated at 7.5 W when operated at 125 V. The tungsten filament has a temperature coefficient of resistivity α = 0.0045/°C. When the filament is hot and glowing, its temperature is seven times room temperature (20 °C). What is the resistance of the filament (in ohms) at room temperature? Group of answer choices 1911 1350 1280 5630 4530

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Eirian 4 years 2021-07-29T09:23:53+00:00 1 Answers 299 views 0

Answers ( )

  1. Calantha
    0
    2021-07-29T09:25:11+00:00
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    To solve this problem we will apply the concepts related to resistance as a function of temperature, product of the relationship between the squared voltage and the power. Mathematically this is,

    R = \frac{v^2}{P}

    Here,

    R = Resistance (At function of temperature)

    v = Voltage

    P = Power

    Then we have,

    R at 140°C (7 times room temperature),

    R(140\°C) = \frac{125^2}{7.5}

    R(140\°C) = 2083.33\Omega

    The relationship between normal temperature and increased temperature would then be given by,

    R(140\°C) = R(20\°C)(1 +\alpha (\Delta T))

    R(140\°C) = R(20\°C)(1+(4.5*10^{-3})(140-20))

    R(20\°C) = \frac{2083.33}{1.54}

    R(20\°C) = 1352.81\Omega

    Therefore the correct value of the group of answer is 1350

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