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Punjab Medical Punjab - MET Solved Paper-2011

  • question_answer
    An external resistance\[R\]is connected with a battery of \[emf\,\,V\] and internal resistance\[r\]. Then heat produced in resistance \[R\] will be maximum, if value of \[R\] is

    A) \[r\]                                      

    B) \[r/2\]

    C) \[2r\]                                    

    D)  infinite

    Correct Answer: A

    Solution :

    \[E=i(R+r)\] \[\Rightarrow \]               \[V=i(R+r)\Rightarrow i=\frac{V}{R+r}\] Heat produced\[H={{\left( \frac{V}{r+R} \right)}^{2}}R\] For maximum heat                 \[\frac{dH}{dR}=0\] Differentiating w.r.t.\[R\], we get                 \[0=\frac{d}{dR}{{V}^{2}}[R{{(r+R)}^{-2}}]\]                 \[{{(r+R)}^{-2}}-2R{{(r+R)}^{-3}}=0\]                 \[0=1-\frac{2R}{r+R}\] So,          \[R=r\]


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