Which of the following arrangement of resistors offers minimum effective resistance between points X and Y?
The correct answer is Option 1.
Key Points
Concept:
The effective resistance of resistors in parallel is
\({1 \over R_effective} = {1 \over R_1}+{1 \over R_2}\)
The effective resistance of resistors in Series is
Reffective = R1 + R2
Explanation:
Case 1: R1 = 3 Ω, R2 = 3 Ω, R3 = 3 Ω in parallel
\({1 \over R_effective} = {1 \over 3}+{1 \over 3}+{1 \over 3}\)
\({1 \over R_effective} = {3 \over 3 }\)
R effective = 1 Ω (Minimum)
Case 2: R1 = 3 Ω , R2 = 3 Ω in parallel
\({1 \over R_effective} = {1 \over 3}+{1 \over 3}\)
\({1 \over R_effective} = {2 \over 3 }\)
Reffective = 1.5 Ω
Case 3: R1 = 1 Ω , R2 = 1 Ω in series
R effective = 1 + 1 = 2 Ω
Case 4: R1 = 1 Ω , R2 = 1 Ω, R3 in series
R effective = 1 + 1 +1 = 3 Ω (Maximum)
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