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If a wire is stretched to quadruple its length without changing its area, what will happen to its resistivity?
It halves.
It quadruples.
It remains the same.
It doubles.
It remains the same.
Resistivity is an intrinsic property of a material that depends only on the nature of the substance and its temperature, not on its dimensions. Stretching a wire changes its resistance (which is an extrinsic property), but the resistivity of the material remains constant.
Resistivity is an intrinsic property of a material that depends only on the nature of the substance and its temperature, not on its dimensions. Stretching a wire changes its resistance (which is an extrinsic property), but the resistivity of the material remains constant.
Think of resistivity like the 'density' of a material. If you stretch a piece of play-dough into a long thin string, its total mass remains the same and its 'density' (how closely the particles are packed) stays the same, even though its shape and dimensions have changed.
R=╧БALтАЛ тАФ Relation between resistance, resistivity, length, and area
╧Б=ne2╧ДmтАЛ тАФ Fundamental definition of resistivity based on electron properties
The resistance R of a conductor is given by R=╧БALтАЛ, where ╧Б is the resistivity. While stretching the wire increases length L and decreases cross-sectional area A (thereby increasing R), ╧Б is solely a characteristic of the electronic structure of the material. Since the material remains the same, ╧Б does not change.
Resistivity (╧Б) is an intensive property of the material.
Resistance (R) depends on geometry (L and A), but resistivity does not.
Stretching a wire changes its length and area, resulting in a change in R, but the atomic nature remains identical.
Used in material science to classify conductors and insulators.
Used in calculating the resistance of custom-length components in circuit design.
The SI unit of resistivity is Ohm-meter (╬йтЛЕm).
Option B (quadruples) is incorrect because it confuses Resistance (RтИЭL2) with Resistivity (constant).
C is correct тАФ Resistivity is an intrinsic material property that remains unchanged regardless of the physical dimensions of the wire.
Remember that 'Intrinsic' properties (Resistivity, Density, Specific Heat Capacity) never change with size/shape, while 'Extrinsic' properties (Resistance, Mass, Heat Capacity) always scale with geometry.
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