Q112 / 150 · MHT CET 2025 (20 Apr Shift 2) · Physics
In an n-p-n transistor amplifier, the collector current is 9 mA . If $90 \%$ of the electrons emitted reach the collector, then
- A$\alpha=9, \beta=0.9$
- B$\alpha=0.9, \beta=90$
- Correct answerC$\alpha=0.9, \beta=9$
- D$\alpha=90, \beta=0.9$
Solution
The ratio of collector current to emitter current is $\alpha = I_C / I_E$. Given that $90\%$ of emitter current reaches the collector, $I_C = 0.9 I_E$, so $\alpha = 0.9$.
The current gain $\beta$ relates to $\alpha$ as $\beta = \frac{\alpha}{1 - \alpha}$. Substituting $\alpha = 0.9$ yields $\beta = \frac{0.9}{1 - 0.9} = \frac{0.9}{0.1} = 9$.
The correct option is $\alpha = 0.9$, $\beta = 9$.
Answer: C
Hence, the correct answer is option: 'C'.