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Which one of the following schematic graphs correctly represents quali

June 1, 2025 by rawan239

Which one of the following schematic graphs correctly represents qualitatively the variation of resistivity ρ with respect to temperature T for a semiconductor?

Graph (a)

Graph (b)

Graph (c)

Graph (d)

This question was previously asked in

UPSC Geoscientist – 2023

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The correct answer is (B) Graph (b).

For a semiconductor, resistivity generally decreases as temperature increases. This is because increasing thermal energy excites more electrons into the conduction band and creates more holes in the valence band, increasing the number of free charge carriers available for conduction. More charge carriers lead to higher conductivity and thus lower resistivity. Graph (b) qualitatively shows this inverse relationship where resistivity decreases with increasing temperature.

In contrast, for a typical metal, resistivity increases with increasing temperature due to increased scattering of electrons by lattice vibrations. Insulators have very high resistivity that changes significantly with temperature, usually decreasing as temperature increases, but starting from a much higher value than semiconductors. Graph (a) represents the behavior of a metal, while graphs (c) and (d) do not represent the typical qualitative behavior of a semiconductor over a relevant temperature range.

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