A) \[\alpha =\frac{{{\beta }^{2}}}{1+{{\beta }^{2}}}\]
B) \[\frac{1}{\alpha }=\frac{1}{\beta }+1\]
C) \[\alpha =\frac{\beta }{1-\beta }\]
D) \[\alpha =\frac{\beta }{1+\beta }\]
Correct Answer: A , C
Solution :
\[\alpha =\frac{{{I}_{C}}}{{{I}_{e}}},\beta =\frac{{{I}_{C}}}{{{I}_{b}}}\] \[{{I}_{e}}={{I}_{b}}+{{I}_{c}}\] \[\Rightarrow \]\[\frac{{{I}_{e}}}{{{I}_{c}}}=\frac{{{I}_{b}}}{{{I}_{c}}}+1\Rightarrow \frac{1}{\alpha }=\frac{1}{\beta }+1\]\[\Rightarrow \]\[\alpha =\frac{\beta }{1+\beta }\]Solution :
\[\alpha =\frac{{{I}_{C}}}{{{I}_{e}}},\beta =\frac{{{I}_{C}}}{{{I}_{b}}}\] \[{{I}_{e}}={{I}_{b}}+{{I}_{c}}\] \[\Rightarrow \]\[\frac{{{I}_{e}}}{{{I}_{c}}}=\frac{{{I}_{b}}}{{{I}_{c}}}+1\Rightarrow \frac{1}{\alpha }=\frac{1}{\beta }+1\]\[\Rightarrow \]\[\alpha =\frac{\beta }{1+\beta }\]
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