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2M length of resistance wire , area of cross section of 0.5.mm2 , as a resistance of 2.20 ohm, calculate , the resistivity of the metal , the lenght of the wire which connected in parallelwith 2 m length wire will give a resistance 2.0 ohm
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2M length of resistance wire , area of cross section of 0.5.mm2 , as a...
**Calculating the Resistivity of the Metal:**
The resistivity (ρ) of a material is a measure of its inherent resistance to the flow of electric current. It is a property that depends on the material and can be used to calculate the resistance of a wire of a given length and cross-sectional area.
Given:
- Length of the resistance wire = 2 m
- Area of cross section = 0.5 mm²
- Resistance of the wire = 2.20 Ω
The formula for calculating resistance using resistivity is:
Resistance (R) = (ρ * Length) / Area
Rearranging the formula, we get:
ρ = (R * Area) / Length
Substituting the given values into the formula:
ρ = (2.20 Ω * 0.5 mm²) / 2 m
Converting mm² to m²:
Area = 0.5 mm² = 0.5 * 10^(-6) m²
Substituting the values again:
ρ = (2.20 Ω * 0.5 * 10^(-6) m²) / 2 m
Simplifying:
ρ = 1.10 * 10^(-6) Ω * m²
Therefore, the resistivity of the metal is 1.10 * 10^(-6) Ω * m².
**Calculating the Length of Wire in Parallel:**
To find the length of the wire that, when connected in parallel with the 2 m length wire, will give a resistance of 2.0 Ω, we can use the formula for the total resistance of parallel resistors. In parallel, the reciprocal of the total resistance is equal to the sum of the reciprocals of the individual resistances.
Given:
- Resistance of the wire = 2.0 Ω
The formula for calculating the total resistance in parallel is:
1 / R(total) = 1 / R1 + 1 / R2
Where R1 is the resistance of the 2 m length wire and R2 is the resistance of the additional wire.
Substituting the given values into the formula:
1 / 2.0 Ω = 1 / 2.20 Ω + 1 / R2
Simplifying:
1 / R2 = 1 / 2.0 Ω - 1 / 2.20 Ω
Calculating the reciprocal:
R2 = 1 / (1 / 2.0 Ω - 1 / 2.20 Ω)
Simplifying:
R2 ≈ 44 Ω
Therefore, the additional wire needed to be connected in parallel with the 2 m length wire to give a resistance of 2.0 Ω is approximately 44 Ω.
In summary, the resistivity of the metal is 1.10 * 10^(-6) Ω * m², and to achieve a resistance of 2.0 Ω, an additional wire of approximately 44 Ω needs to be connected in parallel with the 2 m length wire.
The resistivity (ρ) of a material is a measure of its inherent resistance to the flow of electric current. It is a property that depends on the material and can be used to calculate the resistance of a wire of a given length and cross-sectional area.
Given:
- Length of the resistance wire = 2 m
- Area of cross section = 0.5 mm²
- Resistance of the wire = 2.20 Ω
The formula for calculating resistance using resistivity is:
Resistance (R) = (ρ * Length) / Area
Rearranging the formula, we get:
ρ = (R * Area) / Length
Substituting the given values into the formula:
ρ = (2.20 Ω * 0.5 mm²) / 2 m
Converting mm² to m²:
Area = 0.5 mm² = 0.5 * 10^(-6) m²
Substituting the values again:
ρ = (2.20 Ω * 0.5 * 10^(-6) m²) / 2 m
Simplifying:
ρ = 1.10 * 10^(-6) Ω * m²
Therefore, the resistivity of the metal is 1.10 * 10^(-6) Ω * m².
**Calculating the Length of Wire in Parallel:**
To find the length of the wire that, when connected in parallel with the 2 m length wire, will give a resistance of 2.0 Ω, we can use the formula for the total resistance of parallel resistors. In parallel, the reciprocal of the total resistance is equal to the sum of the reciprocals of the individual resistances.
Given:
- Resistance of the wire = 2.0 Ω
The formula for calculating the total resistance in parallel is:
1 / R(total) = 1 / R1 + 1 / R2
Where R1 is the resistance of the 2 m length wire and R2 is the resistance of the additional wire.
Substituting the given values into the formula:
1 / 2.0 Ω = 1 / 2.20 Ω + 1 / R2
Simplifying:
1 / R2 = 1 / 2.0 Ω - 1 / 2.20 Ω
Calculating the reciprocal:
R2 = 1 / (1 / 2.0 Ω - 1 / 2.20 Ω)
Simplifying:
R2 ≈ 44 Ω
Therefore, the additional wire needed to be connected in parallel with the 2 m length wire to give a resistance of 2.0 Ω is approximately 44 Ω.
In summary, the resistivity of the metal is 1.10 * 10^(-6) Ω * m², and to achieve a resistance of 2.0 Ω, an additional wire of approximately 44 Ω needs to be connected in parallel with the 2 m length wire.
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2M length of resistance wire , area of cross section of 0.5.mm2 , as a resistance of 2.20 ohm, calculate , the resistivity of the metal , the lenght of the wire which connected in parallelwith 2 m length wire will give a resistance 2.0 ohm
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2M length of resistance wire , area of cross section of 0.5.mm2 , as a resistance of 2.20 ohm, calculate , the resistivity of the metal , the lenght of the wire which connected in parallelwith 2 m length wire will give a resistance 2.0 ohm 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 2M length of resistance wire , area of cross section of 0.5.mm2 , as a resistance of 2.20 ohm, calculate , the resistivity of the metal , the lenght of the wire which connected in parallelwith 2 m length wire will give a resistance 2.0 ohm covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 2M length of resistance wire , area of cross section of 0.5.mm2 , as a resistance of 2.20 ohm, calculate , the resistivity of the metal , the lenght of the wire which connected in parallelwith 2 m length wire will give a resistance 2.0 ohm .
2M length of resistance wire , area of cross section of 0.5.mm2 , as a resistance of 2.20 ohm, calculate , the resistivity of the metal , the lenght of the wire which connected in parallelwith 2 m length wire will give a resistance 2.0 ohm 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 2M length of resistance wire , area of cross section of 0.5.mm2 , as a resistance of 2.20 ohm, calculate , the resistivity of the metal , the lenght of the wire which connected in parallelwith 2 m length wire will give a resistance 2.0 ohm covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 2M length of resistance wire , area of cross section of 0.5.mm2 , as a resistance of 2.20 ohm, calculate , the resistivity of the metal , the lenght of the wire which connected in parallelwith 2 m length wire will give a resistance 2.0 ohm .
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