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n equal resistors are first connected in series and then connected in parallel. What is the ratio of the maximum to the minimum resistance?

Asked in CBSE AIPMT 1989 · Series and parallel combinations

(1) n
(2) 1/(n²)
(3) n²
(4) 1/n

Answer: (3) n²

Step-by-step solution

Maximum (series): Rₛ=nR.

Minimum (parallel): Rₚ=R/n.

(Rₛ)/(Rₚ)=(nR)/(R/n)=n².

Why the other options are wrong

(1) Takes the parallel value as R instead of R/n, so the ratio is only nR:R.
(2) Gives minimum to maximum, the inverse of what is asked.
(4) No single slip gives 1/n: it needs the ratio inverted and the parallel value taken as R, two slips at once. A maximum-to-minimum ratio cannot be below 1.

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