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Resistance of metal wire of length 2m is 40ohm.If the diameter of the wire is 0.3mm,what will be the resistivity of the metal at that temperature?
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Resistance of metal wire of length 2m is 40ohm.If the diameter of the ...
Answer :
Resistance , R = 40Ω
Length of wire , L = 2m
diameter of circular part of wire ,d = 0.3mm = 0.3 × 10⁻³m
so, base area of wire , A = πr² = πd²/4 [ ∵d = 2r]
= 3.14 × (0.3 × 10⁻³)²/4m²
= 3.14 × 9 × 10⁻⁸/4 m²
= 28.26/4 × 10⁻⁸ m² = 7.06 × 10⁻⁸ m²
Now, use formula,
R = ρL/A
Here, R is the resistance, ρ is the resistivity , L is the length of wire and A is the base area of it .
So , ρ = RA/L = 40Ω × 7.06 × 10⁻⁸m²/2m
ρ = 1.412 × 10⁻⁶ Ωm
Hence, resistivity is 1.412× 10⁻⁶ Ωm.
Hope its help you.
Resistance , R = 40Ω
Length of wire , L = 2m
diameter of circular part of wire ,d = 0.3mm = 0.3 × 10⁻³m
so, base area of wire , A = πr² = πd²/4 [ ∵d = 2r]
= 3.14 × (0.3 × 10⁻³)²/4m²
= 3.14 × 9 × 10⁻⁸/4 m²
= 28.26/4 × 10⁻⁸ m² = 7.06 × 10⁻⁸ m²
Now, use formula,
R = ρL/A
Here, R is the resistance, ρ is the resistivity , L is the length of wire and A is the base area of it .
So , ρ = RA/L = 40Ω × 7.06 × 10⁻⁸m²/2m
ρ = 1.412 × 10⁻⁶ Ωm
Hence, resistivity is 1.412× 10⁻⁶ Ωm.
Hope its help you.
Community Answer
Resistance of metal wire of length 2m is 40ohm.If the diameter of the ...
Calculation of resistivity of a metal wire
Given:
- Length of wire = 2m
- Resistance of wire = 40ohm
- Diameter of wire = 0.3mm
Formula:
- Resistance = (resistivity x length) / area
- Area = πr^2
- Diameter = 2r
Calculation:
- Diameter = 0.3mm = 0.0003m
- Radius = diameter / 2 = 0.00015m
- Area = πr^2 = 3.14 x (0.00015)^2 = 7.07 x 10^-8 m^2
- Resistance = 40ohm
- Length = 2m
- Substitute these values in the formula:
- 40 = (resistivity x 2) / 7.07 x 10^-8
- Rearrange:
- resistivity = (40 x 7.07 x 10^-8) / 2 = 1.414 x 10^-6 ohm-meter
Answer:
- The resistivity of the metal wire at that temperature is 1.414 x 10^-6 ohm-meter.
Given:
- Length of wire = 2m
- Resistance of wire = 40ohm
- Diameter of wire = 0.3mm
Formula:
- Resistance = (resistivity x length) / area
- Area = πr^2
- Diameter = 2r
Calculation:
- Diameter = 0.3mm = 0.0003m
- Radius = diameter / 2 = 0.00015m
- Area = πr^2 = 3.14 x (0.00015)^2 = 7.07 x 10^-8 m^2
- Resistance = 40ohm
- Length = 2m
- Substitute these values in the formula:
- 40 = (resistivity x 2) / 7.07 x 10^-8
- Rearrange:
- resistivity = (40 x 7.07 x 10^-8) / 2 = 1.414 x 10^-6 ohm-meter
Answer:
- The resistivity of the metal wire at that temperature is 1.414 x 10^-6 ohm-meter.
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Resistance of metal wire of length 2m is 40ohm.If the diameter of the wire is 0.3mm,what will be the resistivity of the metal at that temperature?
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Resistance of metal wire of length 2m is 40ohm.If the diameter of the wire is 0.3mm,what will be the resistivity of the metal at that temperature? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Resistance of metal wire of length 2m is 40ohm.If the diameter of the wire is 0.3mm,what will be the resistivity of the metal at that temperature? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Resistance of metal wire of length 2m is 40ohm.If the diameter of the wire is 0.3mm,what will be the resistivity of the metal at that temperature?.
Resistance of metal wire of length 2m is 40ohm.If the diameter of the wire is 0.3mm,what will be the resistivity of the metal at that temperature? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Resistance of metal wire of length 2m is 40ohm.If the diameter of the wire is 0.3mm,what will be the resistivity of the metal at that temperature? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Resistance of metal wire of length 2m is 40ohm.If the diameter of the wire is 0.3mm,what will be the resistivity of the metal at that temperature?.
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