Concept:Electrical insulators have extremely high resistivities (typically \( \ge 10^{10}\ \Omega\cdot\text{m} \)) due to their wide forbidden energy gaps (\( E_g > 5\text{ eV} \)), which prevent thermal generation of free charge carriers.
Formula:$$\rho = \frac{1}{q (n \mu_n + p \mu_p)} \approx \infty \quad (\text{since } n, p \approx 0 \implies \rho \sim 10^{10}\text{ to } 10^{16}\ \Omega\cdot\text{m})$$
Solution:- Materials like fused quartz, mica, and hard rubber have resistivities ranging from \( 10^{10}\ \Omega\cdot\text{m} \) up to \( 10^{16}\ \Omega\cdot\text{m} \).
Why other options are incorrect:- Option A: \( 10^{-8}\text{ to } 10^{-5}\ \Omega\cdot\text{m} \) corresponds to metallic conductors.
- Option C: \( 10^{-3}\text{ to } 10^3\ \Omega\cdot\text{m} \) corresponds to semiconductors.
- Option D: \( 10^2\text{ to } 10^5\ \Omega\cdot\text{m} \) spans high-resistivity intrinsic semiconductors and semi-insulating substrates.
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