Current Electricity: JEE Main Physics Question with Solution
The resistivity (ρ) of semiconductor varies with temperature. Which of the following curve represents the correct behaviour
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Hint 1 of 2
How does increasing temperature affect the charge carrier concentration (n) and resistivity (ρ) of an intrinsic semiconductor?
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Step-by-step solutionView
Correct answer
Resistivity of a semiconductor decreases exponentially with increasing temperature, represented by curve .
Option analysis
Why each option works or fails
A ·
Confusing the behavior of semiconductors with that of metallic conductors, where resistivity increases with temperature. Recognize that in semiconductors, increasing temperature excites significantly more charge carriers across the bandgap, decreasing resistivity.
B ·
None. This correctly illustrates an exponential decrease of resistivity ρ with absolute temperature T. Correctly applies ρ(T)=ρ0eEg/(2kBT), which falls non-linearly toward zero as T increases.
C ·
Assuming resistivity is independent of temperature, or exhibits a constant horizontal profile across all T. Recall that thermal energy strongly affects free carrier concentration in semiconductors, so resistivity cannot be constant.
D ·
Assuming a linear decrease of resistivity with temperature rather than an exponential drop. Use the exponential dependence ρ∝eEg/(2kBT), which produces a downward curve with decreasing slope rather than a straight line.
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Solution
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✓quick_kill
For a semiconductor, carrier density increases exponentially with temperature via n(T)∝e−Eg/(2kBT), causing resistivity to decrease exponentially according to ρ(T)=ρ0eEg/(2kBT), which corresponds to an exponentially decaying curve with a negative temperature coefficient of resistance.
Hints that build this answer step by step
How does increasing temperature affect the charge carrier concentration (n) and resistivity (ρ) of an intrinsic semiconductor?
Carrier concentration increases exponentially across the bandgap, causing resistivity to decrease non-linearly.
Which functional form and graph shape corresponds to the relation ρ(T)=ρ0eEg/(2kBT)?
A smooth, non-linear curve decreasing asymptotically toward the temperature axis ().