When 126 V is applied across a wire of 10 m length and 0.30 mm radius, the current density is $1.4 × 10^4\, A/m^2$. What is the resistivity of the wire?

$9 × 10^{-4}\,Ωm$

The correct answer is Option (3) → $9 × 10^{-4}\,Ωm$

Given:

Voltage: $V = 126\ \text{V}$

Length: $L = 10\ \text{m}$

Radius: $r = 0.30\ \text{mm} = 0.0003\ \text{m}$

Current density: $J = 1.4 \times 10^4\ \text{A/m²}$

Cross-sectional area: $A = \pi r^2 = \pi (0.0003)^2 \approx 2.827 \times 10^{-7}\ \text{m²}$

Current: $I = J \cdot A = 1.4 \times 10^4 \cdot 2.827 \times 10^{-7} \approx 3.958 \times 10^{-3}\ \text{A}$

Resistance of wire: $R = \frac{V}{I} = \frac{126}{3.958 \times 10^{-3}} \approx 3.18 \times 10^4\ \Omega$

Resistivity: $\rho = R \frac{A}{L} = 3.18 \times 10^4 \cdot \frac{2.827 \times 10^{-7}}{10} \approx 8.99 \times 10^{-4}\ \Omega\cdot\text{m}$

∴ Resistivity of the wire ≈ 8.99 × 10⁻⁴ Ω·m