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The error in measuring resistance of a wire is 1% that in measuring radius 1% and that in length one percent then what is the error in measuring resistivity of wire.?
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The error in measuring resistance of a wire is 1% that in measuring ra...
Calculating Error in Measuring Resistivity
Given Errors:
- Error in measuring resistance: 1%
- Error in measuring radius: 1%
- Error in measuring length: 1%
Formula for Resistivity:
The resistivity (ρ) of a wire is calculated using the formula:
ρ = (R * A) / L
where R is the resistance, A is the cross-sectional area, and L is the length of the wire.
Error Propagation Formula:
The error in the resistivity can be calculated using the error propagation formula:
δρ/ρ = sqrt((δR/R)^2 + (δA/A)^2 + (δL/L)^2)
Calculating Error:
- Given that error in measuring resistance (δR/R) = 1%
- Given that error in measuring radius (δA/A) = 1%
- Given that error in measuring length (δL/L) = 1%
Now, substituting these values into the error propagation formula:
δρ/ρ = sqrt((1%^2 + 1%^2 + 1%^2)
δρ/ρ = sqrt(0.01 + 0.01 + 0.01)
δρ/ρ = sqrt(0.03)
δρ/ρ = 0.1732
Therefore, the error in measuring the resistivity of the wire is approximately 0.1732 or 17.32%. This means that the measurement of resistivity can have an error of 17.32% due to the combined errors in measuring resistance, radius, and length of the wire.
Given Errors:
- Error in measuring resistance: 1%
- Error in measuring radius: 1%
- Error in measuring length: 1%
Formula for Resistivity:
The resistivity (ρ) of a wire is calculated using the formula:
ρ = (R * A) / L
where R is the resistance, A is the cross-sectional area, and L is the length of the wire.
Error Propagation Formula:
The error in the resistivity can be calculated using the error propagation formula:
δρ/ρ = sqrt((δR/R)^2 + (δA/A)^2 + (δL/L)^2)
Calculating Error:
- Given that error in measuring resistance (δR/R) = 1%
- Given that error in measuring radius (δA/A) = 1%
- Given that error in measuring length (δL/L) = 1%
Now, substituting these values into the error propagation formula:
δρ/ρ = sqrt((1%^2 + 1%^2 + 1%^2)
δρ/ρ = sqrt(0.01 + 0.01 + 0.01)
δρ/ρ = sqrt(0.03)
δρ/ρ = 0.1732
Therefore, the error in measuring the resistivity of the wire is approximately 0.1732 or 17.32%. This means that the measurement of resistivity can have an error of 17.32% due to the combined errors in measuring resistance, radius, and length of the wire.
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The error in measuring resistance of a wire is 1% that in measuring radius 1% and that in length one percent then what is the error in measuring resistivity of wire.? for Class 11 2025 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The error in measuring resistance of a wire is 1% that in measuring radius 1% and that in length one percent then what is the error in measuring resistivity of wire.? covers all topics & solutions for Class 11 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The error in measuring resistance of a wire is 1% that in measuring radius 1% and that in length one percent then what is the error in measuring resistivity of wire.?.
The error in measuring resistance of a wire is 1% that in measuring radius 1% and that in length one percent then what is the error in measuring resistivity of wire.? for Class 11 2025 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The error in measuring resistance of a wire is 1% that in measuring radius 1% and that in length one percent then what is the error in measuring resistivity of wire.? covers all topics & solutions for Class 11 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The error in measuring resistance of a wire is 1% that in measuring radius 1% and that in length one percent then what is the error in measuring resistivity of wire.?.
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