Correct Answer: Option D

Explanation

Given:  Length of the wire, \( L = 100 \, \text{cm} = 1.0 \, \text{m} \),  Cross-sectional area, \( A = 2.0 \times 10^{-3} \, \text{cm}^2 = 2.0 \times 10^{-7} \, \text{m}^2 \)
 Resistance, \( R = 0.10 \, \Omega \)

The formula for resistivity \( \rho \) is given by:
\(\rho = R \cdot \frac{A}{L}\)

Substituting the values:
\(\rho = 0.10 \, \Omega \cdot \frac{2.0 \times 10^{-7} \, \text{m}^2}{1.0 \, \text{m}} = 2.0 \times 10^{-8} \, \Omega \cdot \text{m}\)

Now, we can find the conductivity \( \sigma \):
\(\sigma = \frac{1}{\rho} = \frac{1}{2.0 \times 10^{-8} \, \Omega \cdot \text{m}} = 5.0 \times 10^{7} \, \Omega^{-1} \cdot \text{m}^{-1}\)

To convert to \( \text{cm}^{-1} \):
\(\sigma = 5.0 \times 10^{7} \, \Omega^{-1} \cdot \text{m}^{-1} \times \left( \frac{1}{100 \, \text{cm}} \right) = 5.0 \times 10^{5} \, \Omega^{-1} \cdot \text{cm}^{-1}\)

Thus, the electrical conductivity is:
\(\sigma = 5.0 \times 10^{5} \, \Omega^{-1} \cdot \text{cm}^{-1}\).

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