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Two wire a and b are made from the same material why a his length l and area of cross section 2A while while b has length to l and area of cross section a divided by 2 find the ratio of the resistance of a to that of b?
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Two wire a and b are made from the same material why a his length l an...
Understanding Resistance
The resistance (R) of a wire can be calculated using the formula:
R = ρ * (L/A)
where:
- ρ = resistivity of the material
- L = length of the wire
- A = area of cross-section
Wire A Specifications
- Length (L) = l
- Area of cross-section (A) = 2A
Using the formula for resistance:
R_a = ρ * (l / (2A))
Wire B Specifications
- Length (L) = 2l
- Area of cross-section (A) = A/2
Using the same formula for resistance:
R_b = ρ * (2l / (A/2))
Calculating Resistance of Wire B
To simplify R_b:
R_b = ρ * (2l * 2/A)
R_b = ρ * (4l / A)
Finding the Ratio of Resistances
To find the ratio R_a to R_b:
R_a / R_b = (ρ * (l / (2A))) / (ρ * (4l / A))
The ρ and l cancel out:
= (1 / (2A)) / (4 / A)
This simplifies to:
= 1 / 8
Final Ratio
The ratio of the resistance of wire A to wire B is:
R_a : R_b = 1 : 8
Conclusion
Thus, the resistance of wire A is 1/8th that of wire B, indicating that wire A is significantly less resistive compared to wire B due to its larger area and shorter length.
The resistance (R) of a wire can be calculated using the formula:
R = ρ * (L/A)
where:
- ρ = resistivity of the material
- L = length of the wire
- A = area of cross-section
Wire A Specifications
- Length (L) = l
- Area of cross-section (A) = 2A
Using the formula for resistance:
R_a = ρ * (l / (2A))
Wire B Specifications
- Length (L) = 2l
- Area of cross-section (A) = A/2
Using the same formula for resistance:
R_b = ρ * (2l / (A/2))
Calculating Resistance of Wire B
To simplify R_b:
R_b = ρ * (2l * 2/A)
R_b = ρ * (4l / A)
Finding the Ratio of Resistances
To find the ratio R_a to R_b:
R_a / R_b = (ρ * (l / (2A))) / (ρ * (4l / A))
The ρ and l cancel out:
= (1 / (2A)) / (4 / A)
This simplifies to:
= 1 / 8
Final Ratio
The ratio of the resistance of wire A to wire B is:
R_a : R_b = 1 : 8
Conclusion
Thus, the resistance of wire A is 1/8th that of wire B, indicating that wire A is significantly less resistive compared to wire B due to its larger area and shorter length.
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Two wire a and b are made from the same material why a his length l and area of cross section 2A while while b has length to l and area of cross section a divided by 2 find the ratio of the resistance of a to that of b?
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Two wire a and b are made from the same material why a his length l and area of cross section 2A while while b has length to l and area of cross section a divided by 2 find the ratio of the resistance of a to that of b? 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 Two wire a and b are made from the same material why a his length l and area of cross section 2A while while b has length to l and area of cross section a divided by 2 find the ratio of the resistance of a to that of b? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two wire a and b are made from the same material why a his length l and area of cross section 2A while while b has length to l and area of cross section a divided by 2 find the ratio of the resistance of a to that of b?.
Two wire a and b are made from the same material why a his length l and area of cross section 2A while while b has length to l and area of cross section a divided by 2 find the ratio of the resistance of a to that of b? 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 Two wire a and b are made from the same material why a his length l and area of cross section 2A while while b has length to l and area of cross section a divided by 2 find the ratio of the resistance of a to that of b? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two wire a and b are made from the same material why a his length l and area of cross section 2A while while b has length to l and area of cross section a divided by 2 find the ratio of the resistance of a to that of b?.
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