If the length of a wire is doubled and its cross – section area decreased to half ,the resistivity of the wire becomes the same ( put true or false) pleas drwls
To determine whether the statement is true or false, we can use the formula for resistivity:
Resistance = (Resistivity * Length) / Cross-sectional area
Let's consider the initial situation where the length of the wire is L and the cross-sectional area is A. The resistance would then be R1 = (Resistivity * L) / A.
Now, if the length of the wire is doubled to 2L and the cross-sectional area is halved to 0.5A, the new resistance would be R2 = (Resistivity * 2L) / 0.5A.
To check if the resistivity remains the same, we need to equate R1 and R2:
(Resistivity * L) / A = (Resistivity * 2L) / 0.5A
Cross-multiplying and canceling equivalent terms, we get:
4(Resistivity * L) = (Resistivity * 2L)
Dividing both sides of the equation by 2L and canceling equivalent terms, we get:
2 = 1
Since 2 is not equal to 1, we can conclude that the resistivity of the wire does not remain the same when the length is doubled and the cross-sectional area is halved. Therefore, the statement is false.