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

Answer 1

The correct option is A

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

Step 1: Given

Note that the formula, $\alpha =\frac{I_c}{I_E}$and $\beta =\frac{I_c}{I_B}$

Step 2: Finding the relation

Therefore, $I_E=I_B+I_c$

Now relation,

$\begin{array}{l}\Rightarrow \frac{I_E}{I_c}=\frac{I_B}{I_c}+\frac{I_c}{I_c}\\ \Rightarrow \frac{1}{\alpha }=\frac{1}{\beta }+1\\ \Rightarrow \frac{1}{\alpha }=\frac{\beta +1}{\beta }\end{array}$

Simplify further,

$\begin{array}{l}\Rightarrow \alpha =\frac{\beta }{\beta +1}\end{array}$

Hence, the correct option is (A).