A wire of length 3.0 m and diameter 1.5 mm has a resistance of 1.25 Ù. What is the resistivity of the material used to make the wire? A)3.0 × 10^-6 Ù m B)7.4 × 10^-7 Ù m C)1.8 × 10^-7 Ù m D)9.4 × 10^-8 Ù m

Question

Quizplus · Accepted Answer

The resistivity ($\rho$) of the material can be calculated using the formula $\rho = R\frac{A}{L}$, where $R$ is the resistance, $A$ is the cross-sectional area of the wire, and $L$ is the length of the wire. The cross-sectional area $A$ of the wire, given its diameter is 1.5 mm (or 0.0015 m), is $\pi r^2 = \pi (0.0015/2)^2$ m$^2$. Substituting the given values and solving for $\rho$ yields a resistivity of approximately $7.4 \times 10^{-7}$ $\Omega m$, which corresponds to choice B.

A Wire of Length 3