JEE Main 2022 — Semiconductors Question with Solution

Given here, $V_{CE}=8 \mathrm{V}$, $I_C=6 \mathrm{mA}$ from $4 \mathrm{mA}$ and $I_B=20 \mu \mathrm{A}$ to $25 \mu \mathrm{A}$

Current gain is the ratio of change in output current divided by change in input current. For common CE (Common Emitter) configuration, it is the ratio of change in collector current divided by change in base current.

Current gain ${\beta }_{av}=\frac{I_C{}^{\text{'}}-I_C}{I_B{}^{\text{'}}-I_B}=\frac{\left(6-4\right) \mathrm{mA}}{\left(25-20\right) \mathrm{\mu A}}=\frac{2 \mathrm{mA}}{5 \mathrm{\mu A}}$

${\beta }_{\mathrm{av}}=\frac{2}{5}\times {10}^3=\frac{2000}{5}=400$