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Question
Given n resistors each of resistance R, how will you combine them to get the (i) maximum (ii) minimum effective resistance? What is the ratio of the maximum to minimum resistance?
Solution
Total number of resistors = n
Resistance of each resistor = R
(i) When n resistors are connected in series, effective resistance R1 is the maximum, given by the product nR.
Hence, the maximum resistance of the combination, R1 = nR
(ii) When n resistors are connected in parallel, the effective resistance (R2) is the minimum, given by the ratio `"R"/"n"`.
Hence, minimum resistance of the combination, R2 = `"R"/"n"`
The ratio of the maximum to the minimum resistance is,
`"R"_1/"R"_2 = ("nR")/("R"/"n") = "n"^2`
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