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Two wires of the same material are given. The first wire is twice as long as the second and has twice the diameter of the second. The resistance of the first will be
- a)Twice of the second
- b)Half of the second
- c)Equal to the second
- d)Four times of the second
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Two wires of the same material are given. The first wire is twice as l...
Explanation:
Resistance (R) of a wire is directly proportional to its length (l) and inversely proportional to its cross-sectional area (A).
R = ρ * l / A
where ρ is the resistivity of the material.
Given that the first wire is twice as long as the second wire and has twice the diameter of the second wire.
Length of the first wire = 2 * length of the second wire
Diameter of the first wire = 2 * diameter of the second wire
Area of cross-section of the first wire = π * (2 * radius of second wire)² = 4 * π * (radius of second wire)²
Area of cross-section of the second wire = π * (radius of second wire)²
The ratio of the areas of cross-section of the wires is:
4 * π * (radius of second wire)² / π * (radius of second wire)² = 4
Therefore, the ratio of the resistances of the wires is:
R₁ / R₂ = (ρ * 2l₂) / (ρ * l₂ / 4)
R₁ / R₂ = 8
R₁ = 8 * R₂
Hence, the resistance of the first wire is half of the second wire. Therefore, option B is the correct answer.
Resistance (R) of a wire is directly proportional to its length (l) and inversely proportional to its cross-sectional area (A).
R = ρ * l / A
where ρ is the resistivity of the material.
Given that the first wire is twice as long as the second wire and has twice the diameter of the second wire.
Length of the first wire = 2 * length of the second wire
Diameter of the first wire = 2 * diameter of the second wire
Area of cross-section of the first wire = π * (2 * radius of second wire)² = 4 * π * (radius of second wire)²
Area of cross-section of the second wire = π * (radius of second wire)²
The ratio of the areas of cross-section of the wires is:
4 * π * (radius of second wire)² / π * (radius of second wire)² = 4
Therefore, the ratio of the resistances of the wires is:
R₁ / R₂ = (ρ * 2l₂) / (ρ * l₂ / 4)
R₁ / R₂ = 8
R₁ = 8 * R₂
Hence, the resistance of the first wire is half of the second wire. Therefore, option B is the correct answer.
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Two wires of the same material are given. The first wire is twice as long as the second and has twice the diameter of the second. The resistance of the first will bea) Twice of the second b) Half of the second c) Equal to the second d) Four times of the second Correct answer is option 'B'. Can you explain this answer?
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Two wires of the same material are given. The first wire is twice as long as the second and has twice the diameter of the second. The resistance of the first will bea) Twice of the second b) Half of the second c) Equal to the second d) Four times of the second Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two wires of the same material are given. The first wire is twice as long as the second and has twice the diameter of the second. The resistance of the first will bea) Twice of the second b) Half of the second c) Equal to the second d) Four times of the second Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two wires of the same material are given. The first wire is twice as long as the second and has twice the diameter of the second. The resistance of the first will bea) Twice of the second b) Half of the second c) Equal to the second d) Four times of the second Correct answer is option 'B'. Can you explain this answer?.
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