Question

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

Answer 1

Since, $\beta =\frac{\alpha }{1-\alpha }\Rightarrow \alpha \beta =\frac{{\alpha }^2}{1-\alpha }$
$\beta -\alpha =\frac{\alpha }{1-\alpha }-\alpha =\frac{{\alpha }^2}{1-\alpha }$
$\therefore \left(\frac{\beta -\alpha }{\alpha \beta }\right)=\left(\frac{{\alpha }^2}{1-\alpha }\right)\left(\frac{1-\alpha }{{\alpha }^2}\right)=1$