Question

Correct relation between current gain of common base ($\alpha$) and common collector $\left(\beta \right)$ configuration of a transistor is

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

Answer 1

The correct option is A $\alpha \beta =\beta -1$

We know that,

for common base configuration, current gain,
$\alpha =\frac{I_C}{I_E}$

for common emitter configuration, current gain,
$\gamma =\frac{I_C}{I_B}$

for common collector configuration, current gain,
$\beta =\frac{I_E}{I_B}$

Also,$I_E=I_B+I_C$

$\Rightarrow \frac{I_E}{I_C}=\frac{I_B}{I_C}+1$

$\Rightarrow \frac{1}{\alpha }=\frac{1}{\gamma }+1$

$\Rightarrow \gamma =\frac{\alpha }{1-\alpha }---\left(1\right)$

Again,$I_E=I_B+I_C$

$\Rightarrow \frac{I_E}{I_B}=1+\frac{I_C}{I_B}$

$\Rightarrow \beta =1+\gamma ---\left(2\right)$

From $\left(1\right)$ and $\left(2\right)$,

$\beta =\frac{1}{1-\alpha }$

$\Rightarrow \alpha \beta =\beta -1$

Hence, option $\left(B\right)$ is correct.

Why this Question ? Key idea :- This question tests your basic understanding of relation between current gains of various mode of transistor configuration.