Question

In a transistor amplifier, the two a.c. current gains $\alpha$ and $\beta$ are defined as $\alpha =\delta I_C/\delta I_E$ and $\beta =\delta I_C/\delta I_B$.
The relation between $\alpha$ and $\beta$ is

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

Answer 1

Answer: (C)

$\beta =\frac{\alpha }{1-\alpha }$

$I_E=I_B+I_C$
Differentiate w.r.t. to $I_C$ on both side
$\frac{\delta I_E}{\delta I_C}=\frac{\delta I_B}{\delta I_C}+1$
$\frac{1}{\alpha }=\frac{1}{\beta }+1$
$\Rightarrow \frac{1}{\beta }=\frac{1}{\alpha }-1=\frac{1-\alpha }{\alpha }$
$\therefore \beta =\frac{\alpha }{1-\alpha }$.