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JEE Main & Advanced Sample Paper JEE Main Sample Paper-7

  • question_answer
    A capacitor \[1\,\mu F,\] a resistor 20 and a 4H inductor are connected in parallel to a conductor of length 2m sliding with a constant velocity of 1 m/s. If there exists a magnetic field of 2T directed into the plane of the coil, the power stored in the inductor at \[t=1\] second is [Assume that the Magnetic field was activated at \[t=0\]]

    A)  4 W                                      

    B)  8 W

    C)  12 W                    

    D)  2 W

    Correct Answer: A

    Solution :

    Motional \[emf\] produced \[=B\upsilon \ell =4\] volt Since velocity of the vector is constant, the rate of change in flux will be a constant i.e., \[\frac{di}{dt}=1\,A/s\] Power in the inductor \[={{P}_{L}}=\frac{d}{dt}\left( \frac{1}{2}L{{i}^{2}} \right)=Li\frac{di}{dt}\] \[\Rightarrow \,\,\,{{P}_{L}}=4\times 1\times 1=4\] watt.


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