Question

If $\alpha$ and $\beta$ are the current gain in the $CB$ and $CE$ configurations respectively of the transistor circuit, then $\frac{\beta - \alpha}{\alpha\beta} = $

• A. zero
• B. $1$
• C. $2$
• D. $0.5$

Answer 1

Answer: (B)

Since $\beta = \frac{\alpha}{1-\alpha}$
$ \therefore \alpha\beta = \frac{\alpha^{2}}{1-\alpha} \,\,...\left(i\right)$
$ \beta - \alpha = \frac{\alpha}{1-\alpha} -\alpha$ or
$\beta - \alpha = \frac{\alpha^{2}}{1-\alpha} \,\,...\left(ii\right)$
$ \therefore \frac{\beta-\alpha}{\alpha\beta} = \left(\frac{\alpha^{2}}{1-\alpha}\right)\left(\frac{1-\alpha}{\alpha^{2}} \right) = 1$