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BHU PMT BHU PMT (Screening) Solved Paper-2008

  • question_answer
    A piece of wire of resistance R is cut into n equal parts. These parts are then connected in parallel. If the equivalent resistance of the parallel combination is\[R',\], then (R/R) is

    A)  1/1                                       

    B) \[n/1\]

    C)  \[{{n}^{2}}/1\]                                 

    D) \[1/n\]                

    Correct Answer: C

    Solution :

                     Resistance, \[R=\frac{\rho l}{A}\] If r be the resistance of one cut part, then \[r=\frac{\rho (l/n)}{A}=\frac{R}{n}\] The resistance R' of the parallel combination is given by \[\frac{1}{R'}=\frac{1}{r}+\frac{1}{r}+.....=\frac{n}{r}\] So,          \[R'=\frac{r}{n}=\frac{R/n}{n}=\frac{R}{{{n}^{2}}}\] Hence,  \[\frac{R}{R'}=\frac{{{n}^{2}}}{1}\]


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