Q. In the study of transistor as an amplifier, if $\alpha = I_{c}/I_{e}$ and $\beta = I_{c}/I_{b}$, where $I_{c},I_{b}$ and $I_{e}$ are the collector, base and emitter currents, then
A) $\beta = \frac{1 - \alpha}{\alpha}$
B) $\beta = \frac{\alpha}{1 - \alpha}$
C) $\beta = \frac{\alpha}{1 + \alpha}$
D) $\beta = \frac{1 + \alpha}{\alpha}$
Explanation
(b) As we know $i_{E} = i_{C} + i_{B}$
$\Rightarrow \frac{i_{e}}{i_{c}} = 1 + \frac{i_{b}}{i_{c}} \Rightarrow \frac{1}{\alpha} = 1 + \frac{1}{\beta} \Rightarrow \beta = \frac{\alpha}{1 - \alpha}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.