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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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Two wires of same material have length L and 2L and cross-sectional ar...
Explanation:
Given, two wires of same material
Length of first wire (l1) = L
Length of second wire (l2) = 2L
Cross-sectional area of first wire (A1) = 4A
Cross-sectional area of second wire (A2) = A
Let the specific resistance of the material be ρ.
Resistance of first wire (R1) = ρ(l1/A1)
Resistance of second wire (R2) = ρ(l2/A2)
We have to find the ratio of specific resistance of the material.
Ratio of specific resistance = ρ1/ρ2
We can write ρ1 = R1(A2/l2) and ρ2 = R2(A1/l1)
Substituting the values of R1, R2, A1 and A2, we get
ρ1/ρ2 = (l1/l2)(A2/A1)
ρ1/ρ2 = (L/2L)(A/4A)
ρ1/ρ2 = 1/2
Therefore, the ratio of specific resistance of the material is 1:2.
But the correct answer given is option D, which is 1:1.
This is because the question states that both wires are made of the same material. This means that the specific resistance of the material is the same for both wires. Therefore, the ratio of specific resistance is 1:1.
Hence, the correct answer is option D, which is 1:1.
Given, two wires of same material
Length of first wire (l1) = L
Length of second wire (l2) = 2L
Cross-sectional area of first wire (A1) = 4A
Cross-sectional area of second wire (A2) = A
Let the specific resistance of the material be ρ.
Resistance of first wire (R1) = ρ(l1/A1)
Resistance of second wire (R2) = ρ(l2/A2)
We have to find the ratio of specific resistance of the material.
Ratio of specific resistance = ρ1/ρ2
We can write ρ1 = R1(A2/l2) and ρ2 = R2(A1/l1)
Substituting the values of R1, R2, A1 and A2, we get
ρ1/ρ2 = (l1/l2)(A2/A1)
ρ1/ρ2 = (L/2L)(A/4A)
ρ1/ρ2 = 1/2
Therefore, the ratio of specific resistance of the material is 1:2.
But the correct answer given is option D, which is 1:1.
This is because the question states that both wires are made of the same material. This means that the specific resistance of the material is the same for both wires. Therefore, the ratio of specific resistance is 1:1.
Hence, the correct answer is option D, which is 1:1.
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Two wires of same material have length L and 2L and cross-sectional ar...
Same Material, same specific resistance
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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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