GATE 2017 EC (EC2) – Question 16
A connection consists of resistance A in series with a parallel combination of resistances B and C. Three resistors of values $10\ \Omega$, $5\ \Omega$ and $2\ \Omega$ are provided. Consider all possible permutations into positions A, B and C. Identify the maximum and minimum possible overall resistances. Their ratio (maximum divided by minimum), up to second decimal place, is ________.
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Correct answer: 2.12 to 2.16
Explanation
The equivalent resistance is $R=A+BC/(B+C)$. Interchanging B and C does not change it, so only three cases are distinct.
For A equal to 10, 5 and 2 Ω, respectively, the resistances are $10+10/7=80/7$, $5+20/12=20/3$, and $2+50/15=16/3$ Ω.
Thus the maximum is $80/7$ Ω and the minimum is $16/3$ Ω. Their ratio is $15/7=2.142857\ldots$, or **2.14**.