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DUMET Medical DUMET Medical Solved Paper-2004

  • question_answer
    A rectangular coil of 20 turns and area of cross section \[25\,\,c{{m}^{2}}\] has a resistance of \[100\,\,\Omega \]. If a magnetic Held which is perpendicular to the plane of coil changes at a rate of 1000 T/s, the current in the coil is :

    A)  1A            

    B)  50 A

    C)  0.5 A           

    D)  5 A

    Correct Answer: C

    Solution :

     Key Idea: Due to changing magnatic field an emf is induced in the coil. From Faradays law of electromagnetic induction, when magnetic flux linked with a circuit changes, an emf is induced in the coil. \[\therefore \] \[\left| e \right|=\frac{d\phi }{dt}=\frac{NA\,dB}{dt}\,(\because \phi =NAB)\] where N is number of turns in the coil, A is area and B is magnetic field. Given \[N=20,\,A=25\,c{{m}^{2}}=25\times {{10}^{-4}}{{m}^{2}}\] \[R=100\,\Omega ,\frac{dB}{dt}=1000\,T/s\] \[\therefore \]Also \[\left| e \right|=IR\] \[\Rightarrow \] \[I=\frac{\left| e \right|}{R}=\frac{NA}{R}\,.\,\,\frac{dB}{dt}\] Putting the given numerical values, we have \[I=\frac{20\times 25\times {{10}^{-4}}}{100}\times 1000\] \[I=0.5\,A\]


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