Question:
The correct relation between $\alpha$ (ratio of collector current to emitter current) and $\beta$ (ratio of collector current to base current) of a transistor is :
Correct Option: , 4
Solution:
$\alpha=\frac{\mathrm{I}_{\mathrm{C}}}{\mathrm{I}_{\mathrm{E}}}, \beta=\frac{\mathrm{I}_{\mathrm{C}}}{\mathrm{I}_{\mathrm{B}}}$
$\mathrm{I}_{\mathrm{E}}=\mathrm{I}_{\mathrm{B}}+\mathrm{I}_{\mathrm{C}}$
$\alpha=\frac{I_{C}}{I_{B}+I_{C}}=\frac{1}{\frac{I_{B}}{I_{C}}+1}$
$\alpha=\frac{1}{\frac{1}{\beta}+1}$
$\alpha=\frac{\beta}{1+\beta}$