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Question: The relation between α and β parameters of current gains for a transistors is given by...

The relation between α and β parameters of current gains for a transistors is given by

A

α=β1−β\alpha = \frac{\beta}{1 - \beta}

B

α=β1+β\alpha = \frac{\beta}{1 + \beta}

C

α=1−ββ\alpha = \frac{1 - \beta}{\beta}

D

α=1+ββ\alpha = \frac{1 + \beta}{\beta}

Answer

α=β1+β\alpha = \frac{\beta}{1 + \beta}

Explanation

Solution

ie=ib+ic⇒ieic=ibic+1⇒1α=1β+1⇒α=β(1+β)i_{e} = i_{b} + i_{c} \Rightarrow \frac{i_{e}}{i_{c}} = \frac{i_{b}}{i_{c}} + 1 \Rightarrow \frac{1}{\alpha} = \frac{1}{\beta} + 1 \Rightarrow \alpha = \frac{\beta}{(1 + \beta)}.