Manipal Engineering Manipal Engineering Solved Paper-2010

  • question_answer
    A circuit area \[0.01\,{{m}^{2}}\] is kept inside a magnetic field which is normal to its plane. The magnetic field changes from 2 T to 1 T in 1 ms. if the resistance of the circuit is 2\[\Omega \]. The amount of heat evolved is

    A)  0.05 J                                   

    B)  50 J

    C)  0.50 J                   

    D)         500 J

    Correct Answer: A

    Solution :

    Induced emf produced in coil                 \[e=\frac{-d\phi }{dt}=\frac{-d}{dt}(BA)\] \[\therefore \]  \[\left| e \right|=A\frac{dB}{dt}=0.01\times \frac{1}{1\times {{10}^{-3}}}\]                 \[\left| e \right|=10\,\,V\] Current produced in coil,                 \[i=\frac{\left| e \right|}{R}=\frac{10}{2}=5\,\,A\] Heat evolved\[={{i}^{2}}Rt={{(5)}^{2}}\times (2)\times 1\times {{10}^{-3}}\]                 \[=0.05\,\,J\]


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