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If a copper wire is stretched to make it s cross sectional radius 0.1percent thinner ,then what is the percentage increase in it's resistance?
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Calculation of Percentage Increase in Resistance due to Thinning of Copper Wire
1. Given Data:
- Initial cross-sectional radius of copper wire: $r$
- Percentage decrease in cross-sectional radius: $0.1\%$
2. Formula for Resistance of a Wire:
- The resistance of a wire is given by the formula: $R = \frac{{\rho \cdot L}}{{A}}$
- Where $R$ is the resistance, $\rho$ is the resistivity of copper, $L$ is the length of the wire, and $A$ is the cross-sectional area of the wire.
3. Effect of Decrease in Cross-sectional Radius:
- If the cross-sectional radius of the wire is decreased by $0.1\%$, the new radius becomes $(1 - 0.001)r = 0.999r$.
4. Calculation of New Cross-sectional Area:
- The new cross-sectional area, $A'$, can be calculated using the formula for the area of a circle: $A' = \pi \cdot (0.999r)^2$.
5. Percentage Increase in Resistance:
- The percentage increase in resistance can be calculated as: $\frac{{R' - R}}{{R}} \times 100\%$, where $R'$ is the new resistance with the decreased radius.
6. Final Calculation:
- Substitute the new values of radius and area into the resistance formula to find the new resistance, $R'$.
- Calculate the percentage increase in resistance using the given formula.
By following these steps, you can determine the percentage increase in resistance of a copper wire when its cross-sectional radius is stretched to make it 0.1% thinner.
1. Given Data:
- Initial cross-sectional radius of copper wire: $r$
- Percentage decrease in cross-sectional radius: $0.1\%$
2. Formula for Resistance of a Wire:
- The resistance of a wire is given by the formula: $R = \frac{{\rho \cdot L}}{{A}}$
- Where $R$ is the resistance, $\rho$ is the resistivity of copper, $L$ is the length of the wire, and $A$ is the cross-sectional area of the wire.
3. Effect of Decrease in Cross-sectional Radius:
- If the cross-sectional radius of the wire is decreased by $0.1\%$, the new radius becomes $(1 - 0.001)r = 0.999r$.
4. Calculation of New Cross-sectional Area:
- The new cross-sectional area, $A'$, can be calculated using the formula for the area of a circle: $A' = \pi \cdot (0.999r)^2$.
5. Percentage Increase in Resistance:
- The percentage increase in resistance can be calculated as: $\frac{{R' - R}}{{R}} \times 100\%$, where $R'$ is the new resistance with the decreased radius.
6. Final Calculation:
- Substitute the new values of radius and area into the resistance formula to find the new resistance, $R'$.
- Calculate the percentage increase in resistance using the given formula.
By following these steps, you can determine the percentage increase in resistance of a copper wire when its cross-sectional radius is stretched to make it 0.1% thinner.
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If a copper wire is stretched to make it s cross sectional radius 0.1percent thinner ,then what is the percentage increase in it's resistance?
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If a copper wire is stretched to make it s cross sectional radius 0.1percent thinner ,then what is the percentage increase in it's resistance? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about If a copper wire is stretched to make it s cross sectional radius 0.1percent thinner ,then what is the percentage increase in it's resistance? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a copper wire is stretched to make it s cross sectional radius 0.1percent thinner ,then what is the percentage increase in it's resistance?.
If a copper wire is stretched to make it s cross sectional radius 0.1percent thinner ,then what is the percentage increase in it's resistance? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about If a copper wire is stretched to make it s cross sectional radius 0.1percent thinner ,then what is the percentage increase in it's resistance? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a copper wire is stretched to make it s cross sectional radius 0.1percent thinner ,then what is the percentage increase in it's resistance?.
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