A wire of 5Ω resistance is drawn out so that its new length is two times the original length. If the resistivity of the wire remains the same and the cross-sectional area is halved, the new resistance is
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Correct Answer: Option B
Explanation:
Let the original length = L1
Let the original resistance = R1 = 5Ω
Let the original resistivity = P1
Let the original area = a1
Let the new length = L2 = 2L1
let the new area = a2 = 1/(2a2)
Let the new resistance = R2
Let the new resistivity = P2
But since the resistivity remains the same,
=> P1 = P2
But a2 = 1/2a1; and L2 = 2L1
= 20Ω
Let the original length = L1
Let the original resistance = R1 = 5Ω
Let the original resistivity = P1
Let the original area = a1
Let the new length = L2 = 2L1
let the new area = a2 = 1/(2a2)
Let the new resistance = R2
Let the new resistivity = P2
But since the resistivity remains the same,
=> P1 = P2
| _L1 |
| _L2 |
But a2 = 1/2a1; and L2 = 2L1
| _L1 |
| _2L1 |
| _L1 |
| _4L1 |
| _a1 x L1 |
= 20Ω