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AFMC AFMC Solved Paper-2009

  • question_answer
    The tungsten filament of an electric lamp has a surface area A and a power rating P. If the emissivity of the filament is i; and a is Stefan's constant, the steady temperature of the filament will be

    A) \[T={{\left( \frac{P}{A\,\varepsilon \,\sigma } \right)}^{4}}\]                       

    B)  \[T=\left( \frac{P}{A\,\varepsilon \,\sigma } \right)\]

    C) \[T={{\left( \frac{A\,\varepsilon \,\sigma }{P} \right)}^{\frac{1}{4}}}\]                    

    D) \[T={{\left( \frac{P}{A\,\varepsilon \,\sigma } \right)}^{\frac{1}{4}}}\]

    Correct Answer: D

    Solution :

    Radiant power P is defined as energy radiated per unit area. ie,      \[P=\frac{Q}{t}=A\varepsilon \sigma {{T}^{4}}\]\[\Rightarrow \]   \[T={{\left( \frac{P}{A\varepsilon \sigma } \right)}^{1/4}}\]


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