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:

• A. $\beta=\frac{\alpha}{1+\alpha}$
• B. $\alpha=\frac{\beta}{1-\alpha}$
• C. $\beta=\frac{1}{1-\alpha}$
• D. $\alpha=\frac{\beta}{1+\beta}$

Answer 1

Answer: (D)

$\alpha=\frac{ I _{ c }}{ I _{ R }}, \beta=\frac{ I _{ C }}{ I _{ B }}$
$I _{ E }= I _{ B }+ I _{C}$
$\alpha=\frac{ I _{ C }}{ I _{ B }+ I _{ C }}=\frac{1}{\frac{ I _{ B }}{ I _{ C }}+1}$
$\alpha=\frac{1}{\frac{1}{\beta}+1}$
$\alpha=\frac{\beta}{1+\beta}$