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Can you explain the answer of this question below:
A uniform resistance wire of length L and diameter d has a resistance R. Another wire of same material has length 4 L and diameter 2 d, the resistance will be
- A:2 R
- B:R
- C:R/2
- D:R/4
The answer is b.
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Most Upvoted Answer
Can you explain the answer of this question below:A uniform resistance...
Explanation:
The resistance of a wire is directly proportional to its length and inversely proportional to the cross-sectional area of the wire.
Let the resistivity of the wire be p and let the length and diameter of the first wire be L and d respectively. Therefore, the resistance of the first wire is given by:
R = p*L/A
where A is the cross-sectional area of the wire which is given by:
A = π*d^2/4
Substituting the value of A in the expression for resistance, we get:
R = 4*p*L/π*d^2
Now let the length and diameter of the second wire be 4L and 2d respectively. Therefore, the cross-sectional area of the wire is given by:
A = π*(2d)^2/4 = 4*π*d^2/4 = π*d^2
The resistance of the second wire is given by:
R' = p*(4L)/π*d^2
Substituting the value of p and A in the expression for R', we get:
R' = R*(4L/L)/(π*d^2/(π*d^2/4))
R' = R*4/1*4/1 = R
Therefore, the resistance of the second wire is the same as the resistance of the first wire, which is R. Hence, option B is correct.
The resistance of a wire is directly proportional to its length and inversely proportional to the cross-sectional area of the wire.
Let the resistivity of the wire be p and let the length and diameter of the first wire be L and d respectively. Therefore, the resistance of the first wire is given by:
R = p*L/A
where A is the cross-sectional area of the wire which is given by:
A = π*d^2/4
Substituting the value of A in the expression for resistance, we get:
R = 4*p*L/π*d^2
Now let the length and diameter of the second wire be 4L and 2d respectively. Therefore, the cross-sectional area of the wire is given by:
A = π*(2d)^2/4 = 4*π*d^2/4 = π*d^2
The resistance of the second wire is given by:
R' = p*(4L)/π*d^2
Substituting the value of p and A in the expression for R', we get:
R' = R*(4L/L)/(π*d^2/(π*d^2/4))
R' = R*4/1*4/1 = R
Therefore, the resistance of the second wire is the same as the resistance of the first wire, which is R. Hence, option B is correct.
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Can you explain the answer of this question below:A uniform resistance...
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Can you explain the answer of this question below:A uniform resistance wire of length L and diameter d has a resistance R. Another wire of same material has length 4 L and diameter 2 d, the resistance will beA:2 RB:RC:R/2D:R/4The answer is b.
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