n resistance is each of resistance R is first connected in series and then in parallel what is the ratio of series and parallel combination​

Question

n resistance is each of resistance R is first connected in series and then in parallel what is the ratio of series and parallel combination​

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Đan Thu 5 months 2021-08-31T10:23:14+00:00 1 Answers 14 views 0

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    2021-08-31T10:24:42+00:00

    Answer:

    The ratio of the ratio of series and parallel combination​ is n²:1.

    Explanation:

    The equivalent resistance in case of series combination is given by :

    R_s=R_1+R_2+.....+R_n=nR ….(1)

    The equivalent resistance in case of parallel combination is given by :

    R_P=\dfrac{1}{R_1}+\dfrac{1}{R_2}+.....+\dfrac{1}{R_n}=\dfrac{R}{n} ….(2)

    Dividing equation (1) and (2) we get :

    \dfrac{R_s}{R_P}=\dfrac{nR}{R/n}\\\\\dfrac{R_s}{R_P}=\dfrac{n^2}{1}\\\\R_s:R_P=n^2:1

    So, the ratio of the ratio of series and parallel combination​ is n²:1. Hence, this is the required solution.

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