Question

The correct relation between $\alpha$ and $\beta$ in a transistor is?

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

Answer 1

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

We know that
$\alpha =\left(\frac{\Delta i_C}{\Delta i_E}\right)$
and $\beta =\left(\frac{\Delta i_C}{\Delta i_B}\right)=\frac{\Delta i_C}{\Delta i_E}\times \frac{\Delta i_E}{\Delta i_B}$
$=\alpha \frac{\Delta i_E}{\Delta i_B}$
But $\Delta i_B=\Delta i_E-\Delta i_C$
From (ii)
$\beta =\alpha \frac{\Delta i_E}{\Delta i_E-\Delta i_C}=\frac{\alpha }{1-\frac{\Delta i_C}{\Delta i_E}}$
$\therefore \beta =\frac{\alpha }{1-\alpha }$.