Question:
For a transistor $\alpha$ and $\beta$ are given as $\alpha=\frac{I_{C}}{I_{E}}$ and $\beta=\frac{I_{C}}{I_{B}} .$ Then the correct relation between $\alpha$ and $\beta$ will be :
Correct Option: , 2
Solution:
$\alpha=\frac{\mathrm{I}_{\mathrm{C}}}{\mathrm{I}_{\mathrm{E}}}, \beta=\frac{\mathrm{I}_{\mathrm{C}}}{\mathrm{I}_{\mathrm{B}}} ; \mathrm{I}_{\mathrm{E}}=\mathrm{I}_{\mathrm{C}}+\mathrm{I}_{\mathrm{B}}$
$\alpha=\frac{\mathrm{I}_{\mathrm{C}}}{\mathrm{I}_{\mathrm{C}}+\mathrm{I}_{\mathrm{B}}}=\frac{\mathrm{I}_{\mathrm{C}} / \mathrm{I}_{\mathrm{B}}}{\frac{\mathrm{I}_{\mathrm{C}}}{\mathrm{I}_{\mathrm{B}}}+1}=\frac{\beta}{\beta+1}+$
$1+\frac{1}{\beta}=\frac{1}{\alpha}$
$\frac{1}{\beta}=\frac{1-\alpha}{\alpha}$
$\beta=\frac{\alpha}{1-\alpha}$