Question

The correct relation between $\alpha$ $($ratio of collector current to emitter current$)$ and $\beta$ $($ratio of collector current to base current$)$ of a transistor is :

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

Answer 1

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

We know that,

$\alpha =\frac{I_C}{I_E}$ and $\beta =\frac{I_C}{I_B}$

$\because I_E=I_B+I_C$

$\therefore \frac{I_E}{I_C}=\frac{I_B}{I_C}+\frac{I_C}{I_C}$

$\Rightarrow \frac{1}{\alpha }=\frac{1}{\beta }+1=\frac{1+\beta }{\beta }$

$\Rightarrow \alpha =\frac{\beta }{1+\beta }$

Therefore, $\left(A\right)$ is the correct answer.