Question

In a transistor amplifier, the two AC current gains $\alpha $ and $ \beta $ are defined as $\alpha=\frac{\partial I_C}{\partial I_E} $ and $ \beta =\frac{\partial I_C}{\partial I_B}$ the relation between $\alpha$ and $\beta$ is

• A. $\beta=\frac{1-\alpha}{\alpha}$
• B. $\beta=\frac{\alpha}{1-\alpha}$
• C. $\beta=\frac{\alpha}{1+\alpha}$
• D. $\beta=\frac{1+\alpha}{\alpha}$

Answer 1

The Correct Option is B

Given, $\alpha=\frac{\partial I_C}{\partial I_E} $ and $ \beta=\frac{\partial I_C}{\partial I_B}$
We know that in a transistor amplifier
$ I_E =I_C +I_B \Rightarrow \partial I_E =\partial I_C +\partial I_B$
Now, $ \beta=\frac{\partial I_C}{\partial I_B}$
$ =\frac{\partial I_C}{\partial I_E - \partial I_C}$
$ =\frac{\partial I_C / \partial I_E}{1-\partial I_C /\partial I_E} $
$\therefore \beta=\frac{\alpha}{1-\alpha}$