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The resistivity of iron is1×10-7ohm−m. The resistance of a iron wire of particular length and thickness is 1 ohm. If the length and the diameter of wire both are doubled, then the resistivity in ohm−m will be [CPMT 1983; DPMT 1999]
- a)1×10-7
- b)2×10-7
- c)4×10-7
- d)8×10-7
Correct answer is option 'A'. Can you explain this answer?
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The resistivity of iron is1×10-7ohm−m. The resistance of a...
Because it is an intensive property
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The resistivity of iron is1×10-7ohm−m. The resistance of a...
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The resistivity of iron is1×10-7ohm−m. The resistance of a...
Given data:
- Resistivity of iron, ρ = 1×10^-7 ohm-m
- Initial resistance, R = 1 ohm
Calculation:
- Resistance of a wire is given by the formula: R = ρ * (L/A), where L is the length of the wire and A is the cross-sectional area.
- Given R = 1 ohm, ρ = 1×10^-7 ohm-m
When length and diameter are doubled:
- Let the new length be 2L and the new diameter be 2r
- The new resistance, R' = ρ * (2L / (π(2r)^2)) = ρ * (2L / (4πr^2)) = (1/2) * ρ * (L / (πr^2))
- But R = ρ * (L / (πr^2))
- Therefore, R' = (1/2) * R
Conclusion:
- So, when the length and diameter of the wire are doubled, the new resistance becomes half of the initial resistance.
- Therefore, the resistivity remains the same, i.e., 1×10^-7 ohm-m.
- Resistivity of iron, ρ = 1×10^-7 ohm-m
- Initial resistance, R = 1 ohm
Calculation:
- Resistance of a wire is given by the formula: R = ρ * (L/A), where L is the length of the wire and A is the cross-sectional area.
- Given R = 1 ohm, ρ = 1×10^-7 ohm-m
When length and diameter are doubled:
- Let the new length be 2L and the new diameter be 2r
- The new resistance, R' = ρ * (2L / (π(2r)^2)) = ρ * (2L / (4πr^2)) = (1/2) * ρ * (L / (πr^2))
- But R = ρ * (L / (πr^2))
- Therefore, R' = (1/2) * R
Conclusion:
- So, when the length and diameter of the wire are doubled, the new resistance becomes half of the initial resistance.
- Therefore, the resistivity remains the same, i.e., 1×10^-7 ohm-m.
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The resistivity of iron is1×10-7ohm−m. The resistance of a iron wire of particular length and thickness is 1 ohm. If the length and the diameter of wire both are doubled, then the resistivity inohm−mwill be [CPMT 1983; DPMT 1999]a)1×10-7b)2×10-7c)4×10-7d)8×10-7Correct answer is option 'A'. Can you explain this answer?
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The resistivity of iron is1×10-7ohm−m. The resistance of a iron wire of particular length and thickness is 1 ohm. If the length and the diameter of wire both are doubled, then the resistivity inohm−mwill be [CPMT 1983; DPMT 1999]a)1×10-7b)2×10-7c)4×10-7d)8×10-7Correct answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The resistivity of iron is1×10-7ohm−m. The resistance of a iron wire of particular length and thickness is 1 ohm. If the length and the diameter of wire both are doubled, then the resistivity inohm−mwill be [CPMT 1983; DPMT 1999]a)1×10-7b)2×10-7c)4×10-7d)8×10-7Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The resistivity of iron is1×10-7ohm−m. The resistance of a iron wire of particular length and thickness is 1 ohm. If the length and the diameter of wire both are doubled, then the resistivity inohm−mwill be [CPMT 1983; DPMT 1999]a)1×10-7b)2×10-7c)4×10-7d)8×10-7Correct answer is option 'A'. Can you explain this answer?.
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