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Question: If \(\alpha\) and \(\beta\) are the current gain in the CB and CE configurations respectively of the...

If α\alpha and β\beta are the current gain in the CB and CE configurations respectively of the transistor circuit, then β−ααβ=\frac{\beta - \alpha}{\alpha\beta} =

A

Zero

B

1

C

2

D

0.50.5

Answer

1

Explanation

Solution

: since β=α1−α\beta = \frac{\alpha}{1 - \alpha}

∴αβ=α21−α\therefore\alpha\beta = \frac{\alpha^{2}}{1 - \alpha}……. (i)

β−α=α1−α−αorβ−α=α21−α\beta - \alpha = \frac{\alpha}{1 - \alpha} - \alpha or\beta - \alpha = \frac{\alpha^{2}}{1 - \alpha}….. (ii)

∴β−ααβ=(α21−α)(1−αα2)=1\therefore\frac{\beta - \alpha}{\alpha\beta} = \left( \frac{\alpha^{2}}{1 - \alpha} \right)\left( \frac{1 - \alpha}{\alpha^{2}} \right) = 1