If n resistors of value R are first connected in series and then in parallel, then the ratio of their series and parallel combination will be
Answers
Answer:
n^2 as when connected in series R will Rn and when parralel it is r/n therefore n^2
Given : n resistors of value R are first connected in series and then in parallel,
To Find : ratio of their series and parallel combination
Solution:
n resistor connected in series
Rs = R₁ + R₂ + R₃ +...................................+ Rₙ
R₁ = R₂ = R₃ = Rₙ = R
=> Rs = R + R + R +...................................+ R ( n times)
=> Rs = nR
1/Rp = 1/R₁ + 1/R₂ + 1/R₃ +...................................+ 1/Rₙ
R₁ = R₂ = R₃ = Rₙ = R
=> 1/Rp = 1/R + 1/R + 1/R +...................................+ 1/R ( n times)
=> 1/Rp = n/R
=> Rp = R/n
Rs / Rp = nR /( R / n)
=> Rs / Rp = n²
ratio of their series and parallel combination will be n²
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