JEE Exam > JEE Questions > A uniform resistance wire of length L and dia...
Start Learning for Free
A uniform resistance wire of length L and diameter d has a resistance R. Another wire of same material has length 4 L and diameter 2 d, the resistance will be
- a)2 R
- 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 |
Verified Answer
A uniform resistance wire of length L and diameter d has a resistance ...
Most Upvoted Answer
A uniform resistance wire of length L and diameter d has a resistance ...
To understand why the resistance of the second wire is the same as the resistance of the first wire, we need to consider the factors that determine the resistance of a wire.
The resistance of a wire is given by the formula:
R = ρ * (L/A)
where R is the resistance, ρ is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire.
1. Resistance of the first wire:
Let's assume the resistivity of the wire material is constant.
For the first wire:
Length (L) = L
Diameter (d) = d
The cross-sectional area of the wire can be calculated using the formula for the area of a circle:
A = π * (d/2)^2 = π * (d^2/4)
Substituting the values into the resistance formula, we get:
R1 = ρ * (L/A) = ρ * (L/(π * (d^2/4)))
2. Resistance of the second wire:
For the second wire:
Length (L) = 4L (four times the length of the first wire)
Diameter (d) = 2d (twice the diameter of the first wire)
The cross-sectional area of the wire can be calculated using the formula for the area of a circle:
A = π * ((2d)/2)^2 = π * (d^2)
Substituting the values into the resistance formula, we get:
R2 = ρ * (4L/π * (d^2))
3. Comparing the resistances:
To compare the resistances of the two wires, we need to simplify the expression for R2 and see if it is equal to R1.
R2 = ρ * (4L/π * (d^2))
= ρ * (4L/(π * (d^2/4)) * (4/4))
= ρ * (4L/(π * (d^2/4)) * (16/16))
= ρ * (16L/(π * d^2))
From the above expression, we can see that R2 is equal to R1.
Therefore, the resistance of the second wire is the same as the resistance of the first wire, which is option B.
The resistance of a wire is given by the formula:
R = ρ * (L/A)
where R is the resistance, ρ is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire.
1. Resistance of the first wire:
Let's assume the resistivity of the wire material is constant.
For the first wire:
Length (L) = L
Diameter (d) = d
The cross-sectional area of the wire can be calculated using the formula for the area of a circle:
A = π * (d/2)^2 = π * (d^2/4)
Substituting the values into the resistance formula, we get:
R1 = ρ * (L/A) = ρ * (L/(π * (d^2/4)))
2. Resistance of the second wire:
For the second wire:
Length (L) = 4L (four times the length of the first wire)
Diameter (d) = 2d (twice the diameter of the first wire)
The cross-sectional area of the wire can be calculated using the formula for the area of a circle:
A = π * ((2d)/2)^2 = π * (d^2)
Substituting the values into the resistance formula, we get:
R2 = ρ * (4L/π * (d^2))
3. Comparing the resistances:
To compare the resistances of the two wires, we need to simplify the expression for R2 and see if it is equal to R1.
R2 = ρ * (4L/π * (d^2))
= ρ * (4L/(π * (d^2/4)) * (4/4))
= ρ * (4L/(π * (d^2/4)) * (16/16))
= ρ * (16L/(π * d^2))
From the above expression, we can see that R2 is equal to R1.
Therefore, the resistance of the second wire is the same as the resistance of the first wire, which is option B.
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
A uniform resistance wire of length L and diameter d has a resistance R. Another wire of same material has length 4 L and diameter 2 d, the resistance will bea)2 Rb)Rc)R/2d)R/4Correct answer is option 'B'. Can you explain this answer?
Question Description
A uniform resistance wire of length L and diameter d has a resistance R. Another wire of same material has length 4 L and diameter 2 d, the resistance will bea)2 Rb)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 A uniform resistance wire of length L and diameter d has a resistance R. Another wire of same material has length 4 L and diameter 2 d, the resistance will bea)2 Rb)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 A uniform resistance wire of length L and diameter d has a resistance R. Another wire of same material has length 4 L and diameter 2 d, the resistance will bea)2 Rb)Rc)R/2d)R/4Correct answer is option 'B'. Can you explain this answer?.
A uniform resistance wire of length L and diameter d has a resistance R. Another wire of same material has length 4 L and diameter 2 d, the resistance will bea)2 Rb)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 A uniform resistance wire of length L and diameter d has a resistance R. Another wire of same material has length 4 L and diameter 2 d, the resistance will bea)2 Rb)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 A uniform resistance wire of length L and diameter d has a resistance R. Another wire of same material has length 4 L and diameter 2 d, the resistance will bea)2 Rb)Rc)R/2d)R/4Correct answer is option 'B'. Can you explain this answer?.
Solutions for A uniform resistance wire of length L and diameter d has a resistance R. Another wire of same material has length 4 L and diameter 2 d, the resistance will bea)2 Rb)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 A uniform resistance wire of length L and diameter d has a resistance R. Another wire of same material has length 4 L and diameter 2 d, the resistance will bea)2 Rb)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
A uniform resistance wire of length L and diameter d has a resistance R. Another wire of same material has length 4 L and diameter 2 d, the resistance will bea)2 Rb)Rc)R/2d)R/4Correct answer is option 'B'. Can you explain this answer?, a detailed solution for A uniform resistance wire of length L and diameter d has a resistance R. Another wire of same material has length 4 L and diameter 2 d, the resistance will bea)2 Rb)Rc)R/2d)R/4Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of A uniform resistance wire of length L and diameter d has a resistance R. Another wire of same material has length 4 L and diameter 2 d, the resistance will bea)2 Rb)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 A uniform resistance wire of length L and diameter d has a resistance R. Another wire of same material has length 4 L and diameter 2 d, the resistance will bea)2 Rb)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