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A wire made of a specific material has a length
l
l and a cross-sectional area
A
A, with a resistance of 6 Ω. What would be the resistance of another wire made of the same material but with a length of
l
/
3
l/3 and a cross-sectional area of
3
A
3A?
l
l and a cross-sectional area
A
A, with a resistance of 6 Ω. What would be the resistance of another wire made of the same material but with a length of
l
/
3
l/3 and a cross-sectional area of
3
A
3A?
Most Upvoted Answer
A wire made of a specific material has a length ll and a cross-section...
Understanding Resistance
Resistance (R) of a wire is determined by the formula:
R = ρ * (l / A)
where:
- R = Resistance
- ρ = Resistivity of the material
- l = Length of the wire
- A = Cross-sectional area
Given Values
- Original wire resistance (R1) = 6 Ω
- Length (l) = l
- Cross-sectional area (A) = A
New Wire Dimensions
- Length of new wire (l2) = l / 3
- Cross-sectional area of new wire (A2) = 3A
Calculating Resistance of the New Wire
1. Resistivity remains constant: Since both wires are made of the same material, the resistivity (ρ) is the same for both wires.
2. Applying the resistance formula:
For the new wire, the resistance (R2) can be calculated as:
R2 = ρ * (l2 / A2)
3. Substituting new values:
R2 = ρ * ((l / 3) / (3A))
4. Simplifying:
R2 = ρ * (l / (3 * 3A))
= ρ * (l / 9A)
5. Relating to original resistance:
Since we know R1 = ρ * (l / A) = 6 Ω, we can express R2 in terms of R1:
R2 = (1/9) * R1 = (1/9) * 6 Ω = 2/3 Ω
Final Resistance
Thus, the resistance of the new wire is:
- R2 = 2/3 Ω
This demonstrates how changes in length and cross-sectional area affect the resistance of a wire.
Resistance (R) of a wire is determined by the formula:
R = ρ * (l / A)
where:
- R = Resistance
- ρ = Resistivity of the material
- l = Length of the wire
- A = Cross-sectional area
Given Values
- Original wire resistance (R1) = 6 Ω
- Length (l) = l
- Cross-sectional area (A) = A
New Wire Dimensions
- Length of new wire (l2) = l / 3
- Cross-sectional area of new wire (A2) = 3A
Calculating Resistance of the New Wire
1. Resistivity remains constant: Since both wires are made of the same material, the resistivity (ρ) is the same for both wires.
2. Applying the resistance formula:
For the new wire, the resistance (R2) can be calculated as:
R2 = ρ * (l2 / A2)
3. Substituting new values:
R2 = ρ * ((l / 3) / (3A))
4. Simplifying:
R2 = ρ * (l / (3 * 3A))
= ρ * (l / 9A)
5. Relating to original resistance:
Since we know R1 = ρ * (l / A) = 6 Ω, we can express R2 in terms of R1:
R2 = (1/9) * R1 = (1/9) * 6 Ω = 2/3 Ω
Final Resistance
Thus, the resistance of the new wire is:
- R2 = 2/3 Ω
This demonstrates how changes in length and cross-sectional area affect the resistance of a wire.
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A wire made of a specific material has a length ll and a cross-sectional area AA, with a resistance of 6 Ω. What would be the resistance of another wire made of the same material but with a length of l/3l/3 and a cross-sectional area of 3A3A?
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A wire made of a specific material has a length ll and a cross-sectional area AA, with a resistance of 6 Ω. What would be the resistance of another wire made of the same material but with a length of l/3l/3 and a cross-sectional area of 3A3A? 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 A wire made of a specific material has a length ll and a cross-sectional area AA, with a resistance of 6 Ω. What would be the resistance of another wire made of the same material but with a length of l/3l/3 and a cross-sectional area of 3A3A? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wire made of a specific material has a length ll and a cross-sectional area AA, with a resistance of 6 Ω. What would be the resistance of another wire made of the same material but with a length of l/3l/3 and a cross-sectional area of 3A3A?.
A wire made of a specific material has a length ll and a cross-sectional area AA, with a resistance of 6 Ω. What would be the resistance of another wire made of the same material but with a length of l/3l/3 and a cross-sectional area of 3A3A? 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 A wire made of a specific material has a length ll and a cross-sectional area AA, with a resistance of 6 Ω. What would be the resistance of another wire made of the same material but with a length of l/3l/3 and a cross-sectional area of 3A3A? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wire made of a specific material has a length ll and a cross-sectional area AA, with a resistance of 6 Ω. What would be the resistance of another wire made of the same material but with a length of l/3l/3 and a cross-sectional area of 3A3A?.
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