Q147 / 150 · MHT CET 2026 (13 April Shift 1) · Physics
Which of the following graph represents the temperature (T) dependence of resistivity ($\rho$) of a semiconductor?
- AA
- Correct answerBB
- CC
- DD
Solution
The resistivity of a semiconductor is given by the relation:
$\rho = \rho_0 e^{\dfrac{E_g}{2k_B T}}$
where $E_g$ is the band gap energy, $k_B$ is the Boltzmann constant, and $T$ is the absolute temperature.
As the temperature $T$ increases, the number density of charge carriers (electrons and holes) increases exponentially because more electrons gain enough thermal energy to jump from the valence band to the conduction band. Consequently, the resistivity $\rho$ decreases exponentially with an increase in temperature.
Graph (B) correctly represents this non-linear (exponential) decrease of resistivity with temperature.
Answer: B
$\rho = \rho_0 e^{\dfrac{E_g}{2k_B T}}$
where $E_g$ is the band gap energy, $k_B$ is the Boltzmann constant, and $T$ is the absolute temperature.
As the temperature $T$ increases, the number density of charge carriers (electrons and holes) increases exponentially because more electrons gain enough thermal energy to jump from the valence band to the conduction band. Consequently, the resistivity $\rho$ decreases exponentially with an increase in temperature.
Graph (B) correctly represents this non-linear (exponential) decrease of resistivity with temperature.
Answer: B
Hence, the correct answer is option: 'B'.