Which of the following arrangement of resistors offers minimum effective resistance between points X and Y?

This question was previously asked in
UPSC NDA-II (General Ability) Official Paper-I (Held On: 03 Sept, 2023)
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  1. F1 Defence Arbaz 22-1-24 D6
  2. F1 Defence Arbaz 22-1-24 D7
  3. F1 Defence Arbaz 22-1-24 D8
  4. F1 Defence Arbaz 22-1-24 D9

Answer (Detailed Solution Below)

Option 1 : F1 Defence Arbaz 22-1-24 D6
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Detailed Solution

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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 = R+ R2

Explanation:

Case 1: R1 = 3 Ω, R2 = 3 Ω, R3 = 3 Ω  in parallel

\({1 \over R_effective} = {1 \over 3}+{1 \over 3}+{1 \over 3}\)

\({1 \over R_effective} = {3 \over 3 }\)

Reffective = 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

Reffective = 1 + 1 = 2 Ω

Case 4: R1 = 1 Ω, R2 = 1 Ω, R3 in series

Reffective = 1 + 1 +1 = 3 Ω  (Maximum)

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