JEE Exam > JEE Questions > The resistance of a wire of uniform diameter ...
Start Learning for Free
The resistance of a wire of uniform diameter d and lengths L is R. The resistance of another wire of the same material but diameter 2d and length 4L will be
- a)2R
- b)R
- c)R/2
- d)R/4
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
The resistance of a wire of uniform diameter d and lengths L is R. The...
Explanation:
- Resistance Formula:
- The resistance of a wire is given by the formula: R = ρ * (L/A), where ρ is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire.
- Relation between Resistance and Diameter:
- The cross-sectional area (A) of a wire is directly proportional to the square of its diameter (d). Therefore, A ∝ d^2.
- Relation between Resistance and Length:
- The resistance (R) of a wire is directly proportional to its length (L). Therefore, R ∝ L.
- Comparison of Wires:
- Let's compare the two wires:
- Wire 1: Diameter = d, Length = L, Resistance = R
- Wire 2: Diameter = 2d, Length = 4L, Resistance = ?
- Calculations:
- For wire 1: A = π*(d/2)^2 = π*(d^2/4)
- Resistance of wire 1: R1 = ρ * (L/A1) = ρ * (L / (π*(d^2/4)))
- For wire 2: A = π*(2d/2)^2 = π*(4d^2/4) = π*d^2
- Resistance of wire 2: R2 = ρ * (4L/A2) = ρ * (4L / (π*d^2))
- Comparison of Resistances:
- R2 = 4 * (ρ * (L / (π*d^2))) = 4 * (R1) = 4R
Therefore, the resistance of the wire with diameter 2d and length 4L will be 4 times the resistance of the wire with diameter d and length L. Hence, the correct answer is (b) R.
- Resistance Formula:
- The resistance of a wire is given by the formula: R = ρ * (L/A), where ρ is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire.
- Relation between Resistance and Diameter:
- The cross-sectional area (A) of a wire is directly proportional to the square of its diameter (d). Therefore, A ∝ d^2.
- Relation between Resistance and Length:
- The resistance (R) of a wire is directly proportional to its length (L). Therefore, R ∝ L.
- Comparison of Wires:
- Let's compare the two wires:
- Wire 1: Diameter = d, Length = L, Resistance = R
- Wire 2: Diameter = 2d, Length = 4L, Resistance = ?
- Calculations:
- For wire 1: A = π*(d/2)^2 = π*(d^2/4)
- Resistance of wire 1: R1 = ρ * (L/A1) = ρ * (L / (π*(d^2/4)))
- For wire 2: A = π*(2d/2)^2 = π*(4d^2/4) = π*d^2
- Resistance of wire 2: R2 = ρ * (4L/A2) = ρ * (4L / (π*d^2))
- Comparison of Resistances:
- R2 = 4 * (ρ * (L / (π*d^2))) = 4 * (R1) = 4R
Therefore, the resistance of the wire with diameter 2d and length 4L will be 4 times the resistance of the wire with diameter d and length L. Hence, the correct answer is (b) R.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
The resistance of a wire of uniform diameter d and lengths L is R. The resistance of another wire of the same material but diameter 2d and length 4L will bea)2Rb)Rc)R/2d)R/4Correct answer is option 'B'. Can you explain this answer?
Question Description
The resistance of a wire of uniform diameter d and lengths L is R. The resistance of another wire of the same material but diameter 2d and length 4L will bea)2Rb)Rc)R/2d)R/4Correct 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 The resistance of a wire of uniform diameter d and lengths L is R. The resistance of another wire of the same material but diameter 2d and length 4L will bea)2Rb)Rc)R/2d)R/4Correct 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 The resistance of a wire of uniform diameter d and lengths L is R. The resistance of another wire of the same material but diameter 2d and length 4L will bea)2Rb)Rc)R/2d)R/4Correct answer is option 'B'. Can you explain this answer?.
The resistance of a wire of uniform diameter d and lengths L is R. The resistance of another wire of the same material but diameter 2d and length 4L will bea)2Rb)Rc)R/2d)R/4Correct 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 The resistance of a wire of uniform diameter d and lengths L is R. The resistance of another wire of the same material but diameter 2d and length 4L will bea)2Rb)Rc)R/2d)R/4Correct 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 The resistance of a wire of uniform diameter d and lengths L is R. The resistance of another wire of the same material but diameter 2d and length 4L will bea)2Rb)Rc)R/2d)R/4Correct answer is option 'B'. Can you explain this answer?.
Solutions for The resistance of a wire of uniform diameter d and lengths L is R. The resistance of another wire of the same material but diameter 2d and length 4L will bea)2Rb)Rc)R/2d)R/4Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of The resistance of a wire of uniform diameter d and lengths L is R. The resistance of another wire of the same material but diameter 2d and length 4L will bea)2Rb)Rc)R/2d)R/4Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The resistance of a wire of uniform diameter d and lengths L is R. The resistance of another wire of the same material but diameter 2d and length 4L will bea)2Rb)Rc)R/2d)R/4Correct answer is option 'B'. Can you explain this answer?, a detailed solution for The resistance of a wire of uniform diameter d and lengths L is R. The resistance of another wire of the same material but diameter 2d and length 4L will bea)2Rb)Rc)R/2d)R/4Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of The resistance of a wire of uniform diameter d and lengths L is R. The resistance of another wire of the same material but diameter 2d and length 4L will bea)2Rb)Rc)R/2d)R/4Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The resistance of a wire of uniform diameter d and lengths L is R. The resistance of another wire of the same material but diameter 2d and length 4L will bea)2Rb)Rc)R/2d)R/4Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup