AMU Medical AMU Solved Paper-1998

  • question_answer
    When each of n identical resistance of resistance r are connected in series, the effective resistance is R. If these resistances are connected in parallel, the effective resistance of the combination will be

    A) \[R{{n}^{2}}\]                

    B)  \[{{n}^{2}}/r\]

    C) \[R{{r}^{2}}\]                

    D)  \[{{r}^{2}}/R\]

    Correct Answer: D

    Solution :

    : \[R=r+r+r+\].................... up to n terms \[\therefore \] \[R=nr\]              ....................................... (i) In parallel, \[\frac{1}{Z}=\frac{1}{r}+\frac{1}{r}+\frac{1}{r}+\]..........................up to\[n\]terms \[\therefore \]\[\frac{1}{Z}=\frac{n}{r}\] Or \[Z=\frac{r}{n}\]               ...................................... (ii) \[RZ=nr\times \frac{r}{n}\]or\[Rz={{r}^{2}}\]or\[Z=\frac{{{r}^{2}}}{R}\]


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