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ElectricalBasic Electrical
PrevNext

Resistivity of a wire depends on

A

length

B

material

C

cross sectional area

D

none of these

Correct Answer

тЪЩя╕П TE тАв Technical Concept & PrincipleElectricalBasic Electrical
Option B

material

Quick Summary:

Resistivity (also known as specific electrical resistance) is an intrinsic property of a material that quantifies how strongly a material opposes the flow of electric current. Unlike resistance, which depends on the physical dimensions of a conductor, resistivity is independent of length and cross-sectional area, depending solely on the material composition and temperature.

тЪЩя╕ПTETechnical SolutionConcept & Principle
ЁЯТб Explanation

Resistivity (also known as specific electrical resistance) is an intrinsic property of a material that quantifies how strongly a material opposes the flow of electric current. Unlike resistance, which depends on the physical dimensions of a conductor, resistivity is independent of length and cross-sectional area, depending solely on the material composition and temperature.

ЁЯФв Key Formulas

R=╧БlAR = \rho \frac{l}{A}R=╧БAlтАЛ тАФ Resistance formula where ╧Б\rho╧Б is resistivity

╧Б=1╧Г\rho = \frac{1}{\sigma}╧Б=╧Г1тАЛ тАФ Relationship between resistivity and conductivity (╧Г\sigma╧Г)

тЪЩя╕П Working Principle

At the microscopic level, resistivity is defined by the relation R=╧БlAR = \rho \frac{l}{A}R=╧БAlтАЛ. Here, ╧Б\rho╧Б (resistivity) is determined by the electron density, the mean free time between collisions of charge carriers (electrons) with the crystal lattice, and the charge of the carriers. Because these factors are determined by the atomic structure of the material, changing the dimensions of the wire does not alter the material's identity or its fundamental scattering characteristics.

ЁЯУМ Key Points
  • тЦ╕

    Resistivity is an intrinsic property; it does not change with geometry.

  • тЦ╕

    The SI unit for resistivity is Ohm-meter (╬йтЛЕm\Omega \cdot m╬йтЛЕm).

  • тЦ╕

    Resistivity is temperature-dependent for metals, generally increasing with temperature.

  • тЦ╕

    Materials with low resistivity are classified as conductors, while those with high resistivity are insulators.

тЬЕ Advantages
  • тЦ╕

    Allows for standardized material comparison independent of geometry.

  • тЦ╕

    Essential for calculating the design parameters of electrical components.

ЁЯЫая╕П Applications / Uses
  • тЦ╕

    Selection of wire materials for power transmission.

  • тЦ╕

    Designing heating elements using high-resistivity alloys like Nichrome.

  • тЦ╕

    Characterization of semiconductor doping levels.

ЁЯУД Additional Information
  • тЦ╕

    For most metals, resistivity ╧БT=╧Б0[1+╬▒(TтИТT0)]\rho_T = \rho_0 [1 + \alpha(T - T_0)]╧БTтАЛ=╧Б0тАЛ[1+╬▒(TтИТT0тАЛ)], where ╬▒\alpha╬▒ is the temperature coefficient of resistance.

  • тЦ╕

    Option A and C are incorrect because length (lll) and cross-sectional area (AAA) affect total resistance, not the material property resistivity.

  • тЦ╕

    Option D is incorrect because resistivity is fundamentally linked to the material's atomic structure.

ЁЯУК Diagram / Illustration
Resistivity Formula
RтЛЕAR \cdot ARтЛЕA
lll
= ╧Б
тЬЕ

B is correct тАФ Resistivity is a material-specific property that does not change based on the physical dimensions of the conductor.

Core Concepts Used
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Intrinsic Material Property Ohm's Law Extensions Charge Carrier Scattering
ЁЯТб EXAM TIP

Always distinguish between Resistance (RRR, measured in ╬й\Omega╬й) and Resistivity (╧Б\rho╧Б, measured in ╬йтЛЕm\Omega\cdot m╬йтЛЕm); resistance is a circuit parameter, whereas resistivity is a material constant.

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