The resistivity of a current-carrying conducting wire is p. If the wire is doubled in length and its area of cross-section is reduced by half, the new resistivity is:

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The resistivity of a current-carrying conducting wire is p. If the wire is doubled in length and its area of cross-section is reduced by half, the new resistivity is:

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AAI ATC Junior Executive 21 Feb 2023 Shift 2 Official Paper

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half that of the old value
same as the old value
double that of the old value
four times that of the old value

Answer 1

Concept:

Resistivity\((\rho)\): The property of a conductor that opposes the flow of electric current through them and independent of the shape and size of the materials but depends on the nature and temperature of the materials is called resistivity.

Unit of resistivity is the ohm-meter (\(\Omega-m\)).
The resistivity of a material depends on its nature and the temperature of the conductor.
The resistivity of a material doesn't depend on its shape and size (length and area).

The resistance is given by:

\(R=\frac{\rho L}{A}\)

Explanation:

From the above discussion, we can say that

The resistivity of the material will not change (remain the same) as it is independent of the length or cross-section of the wire. So, Option 2 is correct.
It is a material attribute rather than a dimensional one.
The resistance will change but resistivity will remain the same.

Hence, the correct answer is Option-2-same as the old value.

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The resistivity of a current-carrying conducting wire is p. If the wire is doubled in length and its area of cross-section is reduced by half, the new resistivity is:

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