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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:
Given data:
- Length of the first wire = 2L (where L is the length of the second wire)
- Diameter of the first wire = 2d (where d is the diameter of the second wire)
Relationship between resistance, length, and diameter:
- Resistance of a wire is directly proportional to its length (R ∝ L)
- Resistance of a wire is inversely proportional to the cross-sectional area of the wire (R ∝ 1/A, where A = πr^2 and r is the radius of the wire)
Calculating the resistance of the first wire:
- As the length of the first wire is twice that of the second wire, the resistance of the first wire will be twice that of the second wire (R1 = 2R2)
- The diameter of the first wire is twice that of the second wire, which means the radius of the first wire is also twice that of the second wire (r1 = 2r2)
- Since resistance is inversely proportional to the cross-sectional area of the wire, and the cross-sectional area is proportional to the square of the radius (A ∝ r^2), the resistance of the first wire will be half that of the second wire (R1 = 2R2)
Therefore, the resistance of the first wire will be half of the second wire.
Given data:
- Length of the first wire = 2L (where L is the length of the second wire)
- Diameter of the first wire = 2d (where d is the diameter of the second wire)
Relationship between resistance, length, and diameter:
- Resistance of a wire is directly proportional to its length (R ∝ L)
- Resistance of a wire is inversely proportional to the cross-sectional area of the wire (R ∝ 1/A, where A = πr^2 and r is the radius of the wire)
Calculating the resistance of the first wire:
- As the length of the first wire is twice that of the second wire, the resistance of the first wire will be twice that of the second wire (R1 = 2R2)
- The diameter of the first wire is twice that of the second wire, which means the radius of the first wire is also twice that of the second wire (r1 = 2r2)
- Since resistance is inversely proportional to the cross-sectional area of the wire, and the cross-sectional area is proportional to the square of the radius (A ∝ r^2), the resistance of the first wire will be half that of the second wire (R1 = 2R2)
Therefore, the resistance of the first wire will be half of the second wire.
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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 secondb)Half of the secondc)Equal to the secondd)Four times of the secondCorrect 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 secondb)Half of the secondc)Equal to the secondd)Four times of the secondCorrect 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 secondb)Half of the secondc)Equal to the secondd)Four times of the secondCorrect 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 secondb)Half of the secondc)Equal to the secondd)Four times of the secondCorrect answer is option 'B'. Can you explain this answer?.
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 secondb)Half of the secondc)Equal to the secondd)Four times of the secondCorrect 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 secondb)Half of the secondc)Equal to the secondd)Four times of the secondCorrect 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 secondb)Half of the secondc)Equal to the secondd)Four times of the secondCorrect answer is option 'B'. Can you explain this answer?.
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