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Five identical wires of resistance each R are arranged in the form of the letter 'A'. The effective resistance between its free ends is 1)10 ohm 2) 3/16 ohm 3) 32/3 ohm 4) 16/3 ohm (B) * 4 ohm 6 ohm (C) 6 Ω, 2 Ω (D) 8 ohm ,1 ohm?
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Five identical wires of resistance each R are arranged in the form of ...
Analysis:
The given arrangement can be simplified by considering the series and parallel combinations of resistors.
Series Combination:
When resistors are connected in series, the total resistance is the sum of individual resistances.
Total resistance of the vertical wires (left side of 'A') = 2R
Total resistance of the horizontal wire (middle of 'A') = R
Total resistance of the inclined wires (right side of 'A') = 2R
Parallel Combination:
When resistors are connected in parallel, the reciprocal of the total resistance is the sum of reciprocals of individual resistances.
Effective resistance of the vertical wires (left side of 'A') = R/2
Effective resistance of the inclined wires (right side of 'A') = R/2
Effective resistance of the parallel combination of inclined wires = R/4
Overall Combination:
The total resistance of the entire 'A' shape can be calculated by considering the series and parallel combinations.
Total resistance = R + R/4 + R = 9R/4
Calculation:
Given that the total resistance is equal to 9R/4 and it is equal to 3 ohms,
9R/4 = 3
R = 4/3 ohms
Therefore, the effective resistance between the free ends of the 'A' shape is 9R/4 = 9*(4/3)/4 = 3 ohms.
Final Answer:
The correct option is 3) 3 ohms.
The given arrangement can be simplified by considering the series and parallel combinations of resistors.
Series Combination:
When resistors are connected in series, the total resistance is the sum of individual resistances.
Total resistance of the vertical wires (left side of 'A') = 2R
Total resistance of the horizontal wire (middle of 'A') = R
Total resistance of the inclined wires (right side of 'A') = 2R
Parallel Combination:
When resistors are connected in parallel, the reciprocal of the total resistance is the sum of reciprocals of individual resistances.
Effective resistance of the vertical wires (left side of 'A') = R/2
Effective resistance of the inclined wires (right side of 'A') = R/2
Effective resistance of the parallel combination of inclined wires = R/4
Overall Combination:
The total resistance of the entire 'A' shape can be calculated by considering the series and parallel combinations.
Total resistance = R + R/4 + R = 9R/4
Calculation:
Given that the total resistance is equal to 9R/4 and it is equal to 3 ohms,
9R/4 = 3
R = 4/3 ohms
Therefore, the effective resistance between the free ends of the 'A' shape is 9R/4 = 9*(4/3)/4 = 3 ohms.
Final Answer:
The correct option is 3) 3 ohms.
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Five identical wires of resistance each R are arranged in the form of the letter 'A'. The effective resistance between its free ends is 1)10 ohm 2) 3/16 ohm 3) 32/3 ohm 4) 16/3 ohm (B) * 4 ohm 6 ohm (C) 6 Ω, 2 Ω (D) 8 ohm ,1 ohm?
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Five identical wires of resistance each R are arranged in the form of the letter 'A'. The effective resistance between its free ends is 1)10 ohm 2) 3/16 ohm 3) 32/3 ohm 4) 16/3 ohm (B) * 4 ohm 6 ohm (C) 6 Ω, 2 Ω (D) 8 ohm ,1 ohm? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Five identical wires of resistance each R are arranged in the form of the letter 'A'. The effective resistance between its free ends is 1)10 ohm 2) 3/16 ohm 3) 32/3 ohm 4) 16/3 ohm (B) * 4 ohm 6 ohm (C) 6 Ω, 2 Ω (D) 8 ohm ,1 ohm? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Five identical wires of resistance each R are arranged in the form of the letter 'A'. The effective resistance between its free ends is 1)10 ohm 2) 3/16 ohm 3) 32/3 ohm 4) 16/3 ohm (B) * 4 ohm 6 ohm (C) 6 Ω, 2 Ω (D) 8 ohm ,1 ohm?.
Five identical wires of resistance each R are arranged in the form of the letter 'A'. The effective resistance between its free ends is 1)10 ohm 2) 3/16 ohm 3) 32/3 ohm 4) 16/3 ohm (B) * 4 ohm 6 ohm (C) 6 Ω, 2 Ω (D) 8 ohm ,1 ohm? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Five identical wires of resistance each R are arranged in the form of the letter 'A'. The effective resistance between its free ends is 1)10 ohm 2) 3/16 ohm 3) 32/3 ohm 4) 16/3 ohm (B) * 4 ohm 6 ohm (C) 6 Ω, 2 Ω (D) 8 ohm ,1 ohm? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Five identical wires of resistance each R are arranged in the form of the letter 'A'. The effective resistance between its free ends is 1)10 ohm 2) 3/16 ohm 3) 32/3 ohm 4) 16/3 ohm (B) * 4 ohm 6 ohm (C) 6 Ω, 2 Ω (D) 8 ohm ,1 ohm?.
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