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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?
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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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