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JEE Main & Advanced JEE Main Paper (Held On 10-Jan-2019 Morning)

  • question_answer
    A potentiometer wire AB having length L and resistance 12 r is joined to a cell D of emf \[\varepsilon \] and internal resistance r. A cell C having emf \[\varepsilon /2\] and internal resistance 3r is connected. The length AJ at which the galvanometer as shown in figure shows no deflection is- [JEE Main Online Paper (Held On 10-Jan-2019 Morning]

    A) \[\frac{11}{12}\,L\]                               

    B) \[\frac{13}{24}\,L\]

    C) \[\frac{5}{12}\,L\]                     

    D)   \[\frac{11}{24}\,L\]

    Correct Answer: B

    Solution :

    y = Potential gradient \[=\,\,\,\frac{1R}{L}\] \[=\,\,\,\frac{\varepsilon }{12r+r}\,\,=\,\,\frac{12r}{L}\] \[=\,\,\,\frac{12}{13}\,\,\frac{\varepsilon }{L}\] At balanced condition emf of cell \[=\,\,y\ell \] \[\frac{\varepsilon }{2}=\,\,\frac{12}{13}\,\,\frac{\varepsilon }{L}\,\times \ell \] \[\ell \,\,=\,\frac{13}{24}\,L\]


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