Resistivity

NCERT Class 12, Chapter 3 relates the resistance of a uniform conductor to its resistivity through $R=\frac{\rho L}{A}$, so resistivity is $\rho =\frac{RA}{L}$. Converting units, the area $A=1{\text{ mm}}^2=1\times 10^{-6}{\text{ m}}^2$ and the length $L=2$ m. Substituting the measured resistance $R=0.034$ ohm gives $\rho =\frac{0.034\times 10^{-6}}{2}=\frac{3.4\times 10^{-8}}{2}=1.7\times 10^{-8}$ ohm metre, the characteristic value for copper. The value $1.7\times 10^{-5}$ ohm metre is wrong because it fails to convert square millimetres to square metres, missing a factor of $10^{-6}$. The value $6.8\times 10^{-8}$ ohm metre is wrong because it multiplies by the length instead of dividing by it. The value $3.4\times 10^{-8}$ ohm metre is wrong because it omits the division by length of 2 m. Resistivity is a temperature-dependent material constant, so the measurement is quoted at room temperature; heating the wire would raise its resistivity and shift the result. In practice the resistance itself is measured accurately using a metre bridge or by plotting a voltage-current graph and taking the slope, while the diameter needed for the area is measured with a screw gauge and squared, making area the most error-prone factor. A magnitude check confirms the result matches the known resistivity of copper, around $1.7\times 10^{-8}$ ohm metre, validating both the arithmetic and the unit conversions.