GATE EC 2017 Set 2 — Question 6
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General Aptitude → Circuit Fundamentals & Theorems → Permutations & Combinations
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Question
A connection is made consisting of resistance in series with a parallel combination of resistances and . Three resistors of value are provided. Consider all possible permutations of the given resistors into the positions , and identify the configurations with maximum possible overall resistance, and also the ones with minimum possible overall resistance. The ratio of maximum to minimum values of the resistances (up to second decimal place) is ________.
Correct answer
2.12 to 2.16
Solution
The total resistance of the circuit is given by:
We are given three resistors: . We need to find the maximum and minimum possible values of by permuting these values into .Case 1: Maximum Resistance
To maximize , the largest resistor should be placed in series ().
Let .
Case 2: Minimum Resistance
To minimize , the smallest resistor should be placed in series ().
Let .
Ratio Calculation:
Rounding to two decimal places, the ratio is .
We are given three resistors: . We need to find the maximum and minimum possible values of by permuting these values into .Case 1: Maximum Resistance
To maximize , the largest resistor should be placed in series ().
Let .
Case 2: Minimum Resistance
To minimize , the smallest resistor should be placed in series ().
Let .
Ratio Calculation:
Rounding to two decimal places, the ratio is .
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