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A certain wire has a resistance R. The resistance of another wire identical with the first and having twice its diameter is;
- a)0.5 R
- b)0.25 R
- c)4 R
- d)2 R
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A certain wire has a resistance R. The resistance of another wire iden...
Resistance of a wire is inversely proportional to the cross−sectional area:
R α 1/A
α 1/πd^2/4
α 1/d^2
R'/R = (d/d')^2
R'= R(d/2d)^2
= R/4
= 0.25 R
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A certain wire has a resistance R. The resistance of another wire iden...
Explanation:
R = ρ * (L/A)
Where:
R = resistance
ρ = resistivity of the material
L = length of the wire
A = cross-sectional area of the wire
Wire 1:
Resistance = R
Diameter = D
Radius = D/2
Area = π * (D/2)^2 = π * (D^2/4) = π * D^2/4
Wire 2:
Resistance = ?
Diameter = 2D (twice the diameter of wire 1)
Radius = 2D/2 = D
Area = π * D^2
Comparing the two wires:
The radius of wire 2 is D, which is twice the radius of wire 1.
The area of wire 2 is π * D^2, which is four times the area of wire 1 (π * D^2/4).
Calculating the resistance of wire 2:
Using the resistance formula, we can write:
Resistance of wire 2 = ρ * (L/Area) = ρ * (L/(π * D^2))
Since the resistivity and length are the same for both wires, we can compare their resistances by comparing their areas.
Comparing the areas:
Area of wire 2/Area of wire 1 = (π * D^2)/(π * D^2/4) = 4
Therefore, the resistance of wire 2 is four times the resistance of wire 1.
Conclusion:
The resistance of another wire identical to the first wire and having twice its diameter is 0.25R, which is option B.
The resistance of a wire depends on its length, cross-sectional area, and resistivity of the material. The resistance can be calculated using the formula:
R = ρ * (L/A)
Where:
R = resistance
ρ = resistivity of the material
L = length of the wire
A = cross-sectional area of the wire
In this question, we are given that the resistance of the first wire is R. Let's assume the length and resistivity of both wires are the same.
Wire 1:
Resistance = R
Diameter = D
Radius = D/2
Area = π * (D/2)^2 = π * (D^2/4) = π * D^2/4
Wire 2:
Resistance = ?
Diameter = 2D (twice the diameter of wire 1)
Radius = 2D/2 = D
Area = π * D^2
Comparing the two wires:
The radius of wire 2 is D, which is twice the radius of wire 1.
The area of wire 2 is π * D^2, which is four times the area of wire 1 (π * D^2/4).
Calculating the resistance of wire 2:
Using the resistance formula, we can write:
Resistance of wire 2 = ρ * (L/Area) = ρ * (L/(π * D^2))
Since the resistivity and length are the same for both wires, we can compare their resistances by comparing their areas.
Comparing the areas:
Area of wire 2/Area of wire 1 = (π * D^2)/(π * D^2/4) = 4
Therefore, the resistance of wire 2 is four times the resistance of wire 1.
Conclusion:
The resistance of another wire identical to the first wire and having twice its diameter is 0.25R, which is option B.
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A certain wire has a resistance R. The resistance of another wire identical with the first and having twice its diameter is;a)0.5 Rb)0.25 Rc)4 Rd)2 RCorrect answer is option 'B'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A certain wire has a resistance R. The resistance of another wire identical with the first and having twice its diameter is;a)0.5 Rb)0.25 Rc)4 Rd)2 RCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A certain wire has a resistance R. The resistance of another wire identical with the first and having twice its diameter is;a)0.5 Rb)0.25 Rc)4 Rd)2 RCorrect answer is option 'B'. Can you explain this answer?.
A certain wire has a resistance R. The resistance of another wire identical with the first and having twice its diameter is;a)0.5 Rb)0.25 Rc)4 Rd)2 RCorrect answer is option 'B'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A certain wire has a resistance R. The resistance of another wire identical with the first and having twice its diameter is;a)0.5 Rb)0.25 Rc)4 Rd)2 RCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A certain wire has a resistance R. The resistance of another wire identical with the first and having twice its diameter is;a)0.5 Rb)0.25 Rc)4 Rd)2 RCorrect answer is option 'B'. Can you explain this answer?.
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