Question:
Three identical resistors are connected in the form of a triangular mesh ABC. If a battery of 12 V is connected across AB, then the ratio of the current flowing through AB to that through ACB is
Three identical resistors are connected in the form of a triangular mesh ABC. If a battery of 12 V is connected across AB, then the ratio of the current flowing through AB to that through ACB is
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In parallel paths, current divides inversely proportional to resistance.
Updated On: Apr 24, 2026
- \(2:1\)
- \(1:1\)
- \(1:3\)
- \(3:1\)
- \(1:2\)
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
Each resistor has resistance \(R\). Between A and B, there is direct path AB (resistance \(R\)) and path ACB (resistance \(R + R = 2R\)).
Step 2: Detailed Explanation:
Current through AB: \(I_{AB} = \frac{V}{R}\)
Current through ACB: \(I_{ACB} = \frac{V}{2R}\)
\(\frac{I_{AB}}{I_{ACB}} = \frac{V/R}{V/2R} = \frac{2}{1} = 2:1\)
Step 3: Final Answer:
Ratio is \(2:1\).
Each resistor has resistance \(R\). Between A and B, there is direct path AB (resistance \(R\)) and path ACB (resistance \(R + R = 2R\)).
Step 2: Detailed Explanation:
Current through AB: \(I_{AB} = \frac{V}{R}\)
Current through ACB: \(I_{ACB} = \frac{V}{2R}\)
\(\frac{I_{AB}}{I_{ACB}} = \frac{V/R}{V/2R} = \frac{2}{1} = 2:1\)
Step 3: Final Answer:
Ratio is \(2:1\).
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