Which, among the following is a unit for resistivity?

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ohm-metre Explanation: Resistivity (also known as specific electrical resistance) is an intrinsic material property that quantifies how strongly a material opposes the flow of electric current. It is mathematically defined by the relationship between the resistance of a conductor, its cross-sectional area, and its length. Working Principle: The resistance $R$ of a conductor is directly proportional to its length $L$ and inversely proportional to its cross-sectional area $A$. The constant of proportionality is the resistivity $ ho$, defined as $ ho = \frac{R \cdot A}{L}$. Substituting units: $ ext{Ohm} \cdot \frac{ ext{m}^2}{ ext{m}} = \Omega \cdot ext{m}$. Key Formulas: $R = ho \frac{L}{A}$ — Resistance based on dimensions; $ ho = \frac{R \cdot A}{L}$ — Definition of resistivity Key Points: Resistivity is an intrinsic property; it does not change with the shape or size of the object.; The SI unit for resistivity is the ohm-meter ($\Omega \cdot m$).; Resistivity is the reciprocal of conductivity ($\sigma = \frac{1}{ ho}$). Advantages: Allows classification of materials into conductors, insulators, and semiconductors.; Essential for calculating the design parameters of electrical wires and cables. Disadvantages: Resistivity is temperature-dependent for most materials, requiring thermal compensation in high-precision circuits. Applications: Selection of materials for heating elements and electrical wiring.; Characterization of semiconductor substrates. Additional Info: Conductivity is measured in Siemens per meter (S/m).. Option A ($\Omega/m$) is dimensionally incorrect as it implies resistance per unit length (linear resistance).. Option B and D involve incorrect powers of meters for the specific material property. Answer: C is correct — The SI unit of resistivity is the ohm-meter ($\Omega \cdot m$), derived from the formula $ ho = \frac{R \cdot A}{L}$. Exam Tip: Always verify units by performing dimensional analysis; for resistivity, resistance ($[\Omega]$) multiplied by area ($[m^2]$) divided by length ($[m]$) always yields $[\Omega \cdot m]$.

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