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For a given transistor, the value of the forward transfer ratio $\beta =50$. Calculatethe ratio of change in collector current to the change in emitter current.

$(a)\;0.98 \\ (b)\;1.25 \\ (c)\;0.098 \\ (d)\;0.5 $
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Given $\beta = 50$. we need to calculate the ratio of change in collector current to the change in emitter current which is nothing but $\alpha$.
For a transistor, the relationship between $\alpha$ and $\beta$ is as follows: $\beta = \large\frac{I_c}{I_B}$ and $\alpha = \large\frac{I_C}{I_E}$, hence $\large\frac{\beta}{\alpha} $$=\large \frac{I_E}{I_B}$
$I_B = I_E - I_C \rightarrow \large\frac{\beta}{\alpha} $$ = \large\frac{1}{1 - \alpha} $$ \rightarrow \beta = \large\frac{\alpha}{1-\alpha}$
$\Rightarrow 50 =\large\frac{ \alpha}{1- \alpha}$
$\quad 50 -50 \alpha= \alpha$
$\Rightarrow \alpha =\large\frac{50}{51}$
$\qquad= 0.98$
answered Jan 28, 2014 by meena.p
edited Jul 14, 2014 by balaji.thirumalai
 

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