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The length of a given cylindrical wire is increased to double of its original length. The percentage increase in the resistance of the wire will be ______%.
Correct answer is '300'. Can you explain this answer?
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The length of a given cylindrical wire is increased to double of its o...
Explanation:
Let the original length of the wire be 'L' and its resistance be 'R'.
Let the radius of the wire be 'r' and its resistivity be 'ρ'.
The resistance of a wire is given by: R = (ρ * L) / A
where A is the cross-sectional area of the wire, given by: A = π * r^2
When the length of the wire is doubled, its new length becomes 2L.
Therefore, the new resistance of the wire can be calculated as follows:
New resistance, R' = (ρ * 2L) / A
Substituting the value of A, we get:
R' = (ρ * 2L) / (π * r^2)
The percentage increase in resistance can be calculated as follows:
Percentage increase in resistance = ((R' - R) / R) * 100
Substituting the values of R and R', we get:
Percentage increase in resistance = (((ρ * 2L) / (π * r^2)) - ((ρ * L) / (π * r^2))) / ((ρ * L) / (π * r^2)) * 100
Simplifying the above expression, we get:
Percentage increase in resistance = ((ρ * L) / (π * r^2)) * 100
Since ρ and π are constants, we can write the percentage increase in resistance as:
Percentage increase in resistance = (L / r^2) * 100
Substituting the given values, we get:
Percentage increase in resistance = (2L / r^2) * 100
Since the length of the wire is doubled, we can write L as 2L/2. Substituting this value, we get:
Percentage increase in resistance = ((2L/2) / r^2) * 100
Simplifying the above expression, we get:
Percentage increase in resistance = 300%
Therefore, the percentage increase in resistance of the wire is 300%.
Let the original length of the wire be 'L' and its resistance be 'R'.
Let the radius of the wire be 'r' and its resistivity be 'ρ'.
The resistance of a wire is given by: R = (ρ * L) / A
where A is the cross-sectional area of the wire, given by: A = π * r^2
When the length of the wire is doubled, its new length becomes 2L.
Therefore, the new resistance of the wire can be calculated as follows:
New resistance, R' = (ρ * 2L) / A
Substituting the value of A, we get:
R' = (ρ * 2L) / (π * r^2)
The percentage increase in resistance can be calculated as follows:
Percentage increase in resistance = ((R' - R) / R) * 100
Substituting the values of R and R', we get:
Percentage increase in resistance = (((ρ * 2L) / (π * r^2)) - ((ρ * L) / (π * r^2))) / ((ρ * L) / (π * r^2)) * 100
Simplifying the above expression, we get:
Percentage increase in resistance = ((ρ * L) / (π * r^2)) * 100
Since ρ and π are constants, we can write the percentage increase in resistance as:
Percentage increase in resistance = (L / r^2) * 100
Substituting the given values, we get:
Percentage increase in resistance = (2L / r^2) * 100
Since the length of the wire is doubled, we can write L as 2L/2. Substituting this value, we get:
Percentage increase in resistance = ((2L/2) / r^2) * 100
Simplifying the above expression, we get:
Percentage increase in resistance = 300%
Therefore, the percentage increase in resistance of the wire is 300%.
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Community Answer
The length of a given cylindrical wire is increased to double of its o...
Volume is constant. So, length is doubled.
Area is halved.
So,
So, percentage increase will be:
Area is halved.
So,
So, percentage increase will be:
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The length of a given cylindrical wire is increased to double of its original length. The percentage increase in the resistance of the wire will be ______%.Correct answer is '300'. Can you explain this answer?
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The length of a given cylindrical wire is increased to double of its original length. The percentage increase in the resistance of the wire will be ______%.Correct answer is '300'. 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 length of a given cylindrical wire is increased to double of its original length. The percentage increase in the resistance of the wire will be ______%.Correct answer is '300'. 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 length of a given cylindrical wire is increased to double of its original length. The percentage increase in the resistance of the wire will be ______%.Correct answer is '300'. Can you explain this answer?.
The length of a given cylindrical wire is increased to double of its original length. The percentage increase in the resistance of the wire will be ______%.Correct answer is '300'. 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 length of a given cylindrical wire is increased to double of its original length. The percentage increase in the resistance of the wire will be ______%.Correct answer is '300'. 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 length of a given cylindrical wire is increased to double of its original length. The percentage increase in the resistance of the wire will be ______%.Correct answer is '300'. Can you explain this answer?.
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