Resistivity

Question

A wire of length 2 m, cross-sectional area 1 mm², and resistivity 1.7 × 10⁻⁸ Ω·m has what resistance?

RankGuru · Accepted Answer

1. **Resistance Formula**: $R = ho \frac{L}{A}$, where $ho$ is resistivity, $L$ is length, and $A$ is area.
2. **Unit Conversion**: Area $A = 1 	ext{ mm}^2 = 1 	imes (10^{-3} 	ext{ m})^2 = 10^{-6} 	ext{ m}^2$.
3. **Identification**: $L = 2 	ext{ m}$ and $ho = 1.7 	imes 10^{-8} 	ext{ } \Omega\cdot	ext{m}$.
4. **Calculation**:
   - $R = \frac{1.7 	imes 10^{-8} 	imes 2}{10^{-6}}$
   - $R = 3.4 	imes 10^{-8} 	imes 10^{6} = 3.4 	imes 10^{-2}$.
5. **Result**: $R = 0.034 	ext{ } \Omega$.

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