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A copper wire of radius r and length l has a resistance of R. A second copper wire with radius 2r and length l is taken, and the two wires are joined in a parallel combination. The resultant resistance of the parallel combination of the two wires will be
- a)5R
- b)5 / 4R
- c)4 / 5R
- d)R / 5
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A copper wire of radius r and length l has a resistance of R. A second...
Wire A
Length = l
Radius = r
Resistance = ρ×l/πr2
Wire B
Length = l
Radius = 2r
Resistance = ρ×l/4πr2
Let Rp = Effective resistance of parallel combination
1/Rp= 1/R1 + 1/R2
1/Rp = 1/ρ × l/πr2+1/ρ × l/4πr2
1/Rp = ρl/5πr2
Rp = R/5
Length = l
Radius = r
Resistance = ρ×l/πr2
Wire B
Length = l
Radius = 2r
Resistance = ρ×l/4πr2
Let Rp = Effective resistance of parallel combination
1/Rp= 1/R1 + 1/R2
1/Rp = 1/ρ × l/πr2+1/ρ × l/4πr2
1/Rp = ρl/5πr2
Rp = R/5
Most Upvoted Answer
A copper wire of radius r and length l has a resistance of R. A second...
Given:
- A copper wire of radius r and length l has a resistance of R.
- A second copper wire with radius 2r and length l is taken.
- The two wires are joined in a parallel combination.
To find: The resultant resistance of the parallel combination of the two wires.
Solution:
Resistance of a wire is given by the formula:
R = ρ * l / A
where ρ is the resistivity of the material, l is the length of the wire, and A is the cross-sectional area of the wire.
Let's assume that the resistivity of copper remains constant for both wires.
Resistance of the first wire:
R1 = ρ * l / πr^2
Resistance of the second wire:
R2 = ρ * l / π(2r)^2
R2 = ρ * l / 4πr^2
The total resistance of the parallel combination is given by the formula:
1/Rt = 1/R1 + 1/R2
Substituting the values of R1 and R2, we get:
1/Rt = πr^2 / ρl + 4πr^2 / ρl
1/Rt = 5πr^2 / ρl
Rt = ρl / 5πr^2
Comparing this with the resistance of the first wire, R = ρl / πr^2, we get:
Rt = R / 5
Therefore, the resultant resistance of the parallel combination of the two wires will be R / 5, which is option D.
- A copper wire of radius r and length l has a resistance of R.
- A second copper wire with radius 2r and length l is taken.
- The two wires are joined in a parallel combination.
To find: The resultant resistance of the parallel combination of the two wires.
Solution:
Resistance of a wire is given by the formula:
R = ρ * l / A
where ρ is the resistivity of the material, l is the length of the wire, and A is the cross-sectional area of the wire.
Let's assume that the resistivity of copper remains constant for both wires.
Resistance of the first wire:
R1 = ρ * l / πr^2
Resistance of the second wire:
R2 = ρ * l / π(2r)^2
R2 = ρ * l / 4πr^2
The total resistance of the parallel combination is given by the formula:
1/Rt = 1/R1 + 1/R2
Substituting the values of R1 and R2, we get:
1/Rt = πr^2 / ρl + 4πr^2 / ρl
1/Rt = 5πr^2 / ρl
Rt = ρl / 5πr^2
Comparing this with the resistance of the first wire, R = ρl / πr^2, we get:
Rt = R / 5
Therefore, the resultant resistance of the parallel combination of the two wires will be R / 5, which is option D.
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A copper wire of radius r and length l has a resistance of R. A second copper wire with radius 2r and length l is taken, and the two wires are joined in a parallel combination. The resultant resistance of the parallel combination of the two wires will bea)5Rb)5 / 4Rc)4 / 5Rd)R / 5Correct answer is option 'D'. Can you explain this answer?
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A copper wire of radius r and length l has a resistance of R. A second copper wire with radius 2r and length l is taken, and the two wires are joined in a parallel combination. The resultant resistance of the parallel combination of the two wires will bea)5Rb)5 / 4Rc)4 / 5Rd)R / 5Correct answer is option 'D'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about A copper wire of radius r and length l has a resistance of R. A second copper wire with radius 2r and length l is taken, and the two wires are joined in a parallel combination. The resultant resistance of the parallel combination of the two wires will bea)5Rb)5 / 4Rc)4 / 5Rd)R / 5Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A copper wire of radius r and length l has a resistance of R. A second copper wire with radius 2r and length l is taken, and the two wires are joined in a parallel combination. The resultant resistance of the parallel combination of the two wires will bea)5Rb)5 / 4Rc)4 / 5Rd)R / 5Correct answer is option 'D'. Can you explain this answer?.
Solutions for A copper wire of radius r and length l has a resistance of R. A second copper wire with radius 2r and length l is taken, and the two wires are joined in a parallel combination. The resultant resistance of the parallel combination of the two wires will bea)5Rb)5 / 4Rc)4 / 5Rd)R / 5Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Defence.
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