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WB JEE Medical WB JEE Medical Solved Paper-2006

  • question_answer
    A uniform wire of resistance R and length L is cut into four equal parts, each of length L/4, which are then connected in parallel combination. The effective resistance of the  combination will be:    

    A)  R                                           

    B)  4R

    C)  \[\frac{R}{4}\]                                 

    D)  \[\frac{R}{16}\]

    Correct Answer: D

    Solution :

                     \[R=\frac{\rho l}{A}\] or            \[R\propto l\] \[\therefore \]  \[\frac{{{R}_{1}}}{{{R}_{2}}}=\frac{{{l}_{1}}}{{{l}_{2}}}=\frac{L}{L/4}=4\] or            \[{{R}_{2}}=\frac{R}{4}\]                               \[(\because \,{{R}_{1}}=R)\] In parallel combination of such four resistances. \[\frac{1}{R}=\frac{1}{{{R}_{2}}}+\frac{1}{{{R}_{2}}}+\frac{1}{{{R}_{2}}}+\frac{1}{{{R}_{2}}}\]                 or            \[\frac{1}{R}=\frac{1}{R/4}+\frac{1}{R/4}+\frac{1}{R/4}+\frac{1}{R/4}\]                 or            \[\frac{1}{R}=\frac{4}{R}+\frac{4}{R}+\frac{4}{R}+\frac{4}{R}\]                 or            \[\frac{1}{R}=\frac{16}{R}\] or            \[R=\frac{R}{16}\]


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