A wire of 5Ω resistance is drawn out so that its ne...
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
40Ω
20Ω
10Ω
5Ω
Correct answer is B
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
∴ P1 = | R1 a1 |
_L1 |
= P2 = | R2 a2 |
_L2 |
∴ | R1 a1 |
_L1 |
= | R2 2a1/2 |
_2L1 |
=> | 5 x a1 |
_L1 |
= | R2 x a1 |
_4L1 |
∴R2 = | 5 x a1 x 4L1 |
_a1 x L1 |