Question

The correct relation between current gains $\alpha$ and $\beta$ is

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

Answer 1

The correct option is A $\beta =\frac{\alpha }{1-\alpha }$

For transistors,
$I_e=I_b+I_c$

$\frac{I_e}{I_c}=\frac{I_b}{I_c}+1$

$\frac{1}{\alpha }=\frac{1}{\beta }+1$ ...... $\because \frac{I_c}{I_e}=\alpha$ and $\frac{I_c}{I_b}=\beta$

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

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

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