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Two wires of same material have length L and 2L and cross-sectional areas 4A and A respectively. The ratio of their specific resistance would be
- a)1 : 2
- b)8 : 1
- c)1 : 8
- d)1 : 1
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Two wires of same material have length L and 2L and cross-sectional ar...
The specific resistance depends on the nature of material and the temperature of material and it is independent of dimensions of the material.
Hence the two given materials has same specific resistance as they are made of same material.
Ratio=1:1
Answer-(D)
Most Upvoted Answer
Two wires of same material have length L and 2L and cross-sectional ar...
Given: Two wires of same material have length L and 2L and cross-sectional areas 4A and A respectively.
To find: The ratio of their specific resistance.
Solution:
The resistance of a wire is given by the formula:
R = ρL/A
where ρ is the specific resistance, L is the length of the wire, and A is the cross-sectional area of the wire.
Let's find the resistance of each wire first.
For the first wire:
R1 = ρL/4A
For the second wire:
R2 = ρ(2L)/A
Now, let's find the ratio of their specific resistance.
ρ1/ρ2 = (R1A)/(R2*4A)
ρ1/ρ2 = (L/4)/(2L/4)
ρ1/ρ2 = 1/2
Therefore, the ratio of their specific resistance is 1:2.
But the given options do not have this answer. Therefore, this means that the given options are wrong.
The correct ratio of their specific resistance is 1:1. This means that both wires have the same specific resistance.
This can be proven by substituting the resistance formulas back into the equation:
R1/R2 = (ρL/4A)/(ρ(2L)/A)
R1/R2 = L/8L
R1/R2 = 1/8
Therefore, R2 = 8R1. This means that the resistance of the second wire is 8 times greater than the resistance of the first wire.
However, since the cross-sectional area of the second wire is 4 times smaller than that of the first wire, the specific resistance of the second wire must be 4 times greater than that of the first wire.
Therefore, the ratio of their specific resistance is 1:1.
Hence, option D is the correct answer.
To find: The ratio of their specific resistance.
Solution:
The resistance of a wire is given by the formula:
R = ρL/A
where ρ is the specific resistance, L is the length of the wire, and A is the cross-sectional area of the wire.
Let's find the resistance of each wire first.
For the first wire:
R1 = ρL/4A
For the second wire:
R2 = ρ(2L)/A
Now, let's find the ratio of their specific resistance.
ρ1/ρ2 = (R1A)/(R2*4A)
ρ1/ρ2 = (L/4)/(2L/4)
ρ1/ρ2 = 1/2
Therefore, the ratio of their specific resistance is 1:2.
But the given options do not have this answer. Therefore, this means that the given options are wrong.
The correct ratio of their specific resistance is 1:1. This means that both wires have the same specific resistance.
This can be proven by substituting the resistance formulas back into the equation:
R1/R2 = (ρL/4A)/(ρ(2L)/A)
R1/R2 = L/8L
R1/R2 = 1/8
Therefore, R2 = 8R1. This means that the resistance of the second wire is 8 times greater than the resistance of the first wire.
However, since the cross-sectional area of the second wire is 4 times smaller than that of the first wire, the specific resistance of the second wire must be 4 times greater than that of the first wire.
Therefore, the ratio of their specific resistance is 1:1.
Hence, option D is the correct answer.
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Community Answer
Two wires of same material have length L and 2L and cross-sectional ar...
Wires of same material have same resistivity
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Two wires of same material have length L and 2L and cross-sectional areas 4A and A respectively. The ratio of their specific resistance would bea)1 : 2b)8 : 1c)1 : 8d)1 : 1Correct answer is option 'D'. Can you explain this answer?
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