Question

For a common emitter configuration, if $\alpha$ and $\beta$ have their usual meanings, the incorrect relationship between $\alpha$ and $\beta$ is

• A. $\begin{array}{c}\frac{1}{\alpha }=\frac{1}{\beta }+1\end{array}$
• B. $\begin{array}{c}\alpha =\frac{\beta }{1-\beta }\end{array}$
• C. $\begin{array}{c}\alpha =\frac{\beta }{1+\beta }\end{array}$
• D. None

Answer 1

The correct option is C $\begin{array}{c}\alpha =\frac{\beta }{1+\beta }\end{array}$

We know, collector current is given as $I_C=\beta I_B$
Also, $I_C=\alpha I_E$
Using, $I_E=I_B+I_C$
$\frac{I_C}{\alpha }=\frac{I_C}{\beta }+I_C$
Solving above equations,
$\frac{1}{\alpha }=1+\frac{1}{\beta }$
$\alpha =\frac{\beta }{1+\beta }$