A given wire of resistance 10 Ω has a length of 5 m and a cross-sectional area of 4.0 × 10\(^{-3}\) m\(^2\). Calculate the conductivity of the wire.
The resistance \(R\) of a wire is related to its resistivity \(\rho\), length \(L\), and cross-sectional area \(A\) by the formula: \(R = \frac{\rho L}{A}\)
The conductivity \(\sigma\) is the reciprocal of the resistivity:
\(\sigma = \frac{1}{\rho}\)
\(\rho = \frac{R A}{L}\)
\(\sigma = \frac{L}{R A}\)
Substitute the given values (\(L = 5\) m, \(R = 10\) Ω, \(A = 4.0 \times 10^{-3}\) m²):
\(\sigma = \frac{5}{10 \times 4.0 \times 10^{-3}} = \frac{5}{0.04} = 125\)
The conductivity of the wire is 125 Ω\(^{-1}\)m\(^{-1}\) = 1.25 x 10\(^2\) Ω\(^{-1}\)m\(^{-1}\)
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