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

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Captcha* Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )

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minhkhang · Answer 1 · 2021-08-31T10:24:42+00:00

minhkhang

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2021-08-31T10:24:42+00:00 August 31, 2021 at 10:24 am

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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.