Question

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

• A. $\frac{1}{\alpha }=\frac{1}{\beta }+1$
• B. $\alpha =\frac{\beta }{1-\beta }$
• C. $\alpha =\frac{\beta }{1+\beta }$
• D. $\alpha =\frac{{\beta }^2}{1+{\beta }^2}$

Answer 1

Answer: (A), (C)

The correct options are
A $\frac{1}{\alpha }=\frac{1}{\beta }+1$
C $\alpha =\frac{\beta }{1+\beta }$

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,

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

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