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I have a doubt, kindly clarify. For a common emitter configuration, if α and β have their usual meanings, the incorrect relationship between α and β is :

 For a common emitter configuration, if α and β have their usual meanings, the incorrect relationship between α and β is :

  • Option 1)

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

  • Option 2)

    \alpha = \frac{\beta }{1-\beta }

  • Option 3)

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

  • Option 4)

    \alpha = \frac{\beta ^{2}}{1+\beta^{2} }

 
Answers (1)
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As we have learnt,

 

Relation between α and β -

\beta = \frac{\alpha }{1-\alpha }
 

- wherein

\alpha = \frac{I_{C}}{I_{E}}

\beta = \frac{I_{C}}{I_{B}} (current gain )

 

 For common emitter configuration 

       \Delta I_E = \Delta I_C + \Delta I_B

\\ or\;\frac{\Delta I_C}{\Delta I_C} + \frac{\Delta I_B}{\Delta I_C} = \frac{\Delta I_E}{\Delta I_C}

\alpha = \frac{\Delta I_C}{\Delta I_E}, \beta = \frac{\Delta I_C}{\Delta I_B}

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

or\; \alpha = \frac{\beta}{1 + \beta}

 

 


Option 1)

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

Option 2)

\alpha = \frac{\beta }{1-\beta }

Option 3)

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

Option 4)

\alpha = \frac{\beta ^{2}}{1+\beta^{2} }

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