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If length of conductor whose volume /mass is constant increases by 3%,then find resistance percent change?
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If length of conductor whose volume /mass is constant increases by 3%,...
Solution:
Given:
Length of conductor increases by 3%
To find:
The percentage change in resistance
Concept Used:
The resistance of a conductor is directly proportional to its length.
Formula:
R = ρ(l/A)
where R is the resistance, ρ is the resistivity of the material, l is the length of the conductor, and A is the cross-sectional area of the conductor.
Calculation:
Let the initial length of the conductor be l1, and the initial resistance be R1.
Then, the initial volume of the conductor will be V1 = Al1, where A is the cross-sectional area of the conductor.
Also, let the final length of the conductor be l2, where l2 = 1.03l1 (since the length increases by 3%).
The final volume of the conductor will remain the same as the initial volume, so we have V1 = Al1 = Al2.
Therefore, the new cross-sectional area will be A2 = A(l1/l2).
Using the formula for resistance, we get:
R2 = ρ(l2/A2)
= ρ(l1/l2)(l2/A)
= ρ(l1/l2)(1.03l1)/A
= 1.03ρl1²/(A(l1/l2))
The percentage change in resistance can be calculated as follows:
% Change in Resistance = ((R2 - R1)/R1) x 100%
= ((1.03ρl1²/(A(l1/l2))) - R1)/R1) x 100%
Substituting A(l1/l2) for A2, we get:
% Change in Resistance = ((1.03ρl1²/A(l1/l2)) - R1)/R1) x 100%
= ((1.03ρl1²/A2) - R1)/R1) x 100%
Final Answer:
Therefore, the percentage change in resistance is ((1.03ρl1²/A2) - R1)/R1) x 100%.
Community Answer
If length of conductor whose volume /mass is constant increases by 3%,...
Here they are tqlking about the exansion of length so can u simplify it a bit extent
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If length of conductor whose volume /mass is constant increases by 3%,then find resistance percent change?
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If length of conductor whose volume /mass is constant increases by 3%,then find resistance percent change? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about If length of conductor whose volume /mass is constant increases by 3%,then find resistance percent change? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If length of conductor whose volume /mass is constant increases by 3%,then find resistance percent change?.
If length of conductor whose volume /mass is constant increases by 3%,then find resistance percent change? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about If length of conductor whose volume /mass is constant increases by 3%,then find resistance percent change? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If length of conductor whose volume /mass is constant increases by 3%,then find resistance percent change?.
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