Maharashtra BoardEnglish MediumSTD 12 SciencePhysicsQuestion Bank [ 2022 ]2 Marks
Question
Define current amplification factor $\alpha _{DC}$ and $\beta_{DC}$ Obtain the relation between them.
✓
Answer
i. In the case of common emitter configuration, common base current gain or the current amplification factor $\left(\alpha_{D C}\right)$ is the ratio of the collector current to the emitter current.
$\alpha_{D C}=\frac{I_c}{I_E} \text {. }$
ii. Similarly, the common-emitter current gain of the current amplification factor $\left(\beta_{D C}\right)$ is defined as the ratio of the collector current to the base current.
$\beta_{D C}=\frac{I_c}{I_B}$
iii. Since, $I _{ E }= I _{ B }+ I _{ C }$
Dividing throughout by $I _{ C }$
$ \frac{ I _{ E }}{ I _{ c }}=\frac{ I _{ B }}{ I _{ c }}+1$
$\therefore \frac{1}{\alpha_{ DC }}=\frac{1}{\beta_{ DC }}+1 \ldots[\text { From (1) and (2)] }$
$\therefore \alpha_{ DC }=\frac{\beta_{ DC }}{1+\beta_{ DC }}$
$\therefore \beta_{ DC }=\frac{\alpha_{ DC }}{1-\alpha_{ DC }} $
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