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 :
Solution
$\alpha = {{{I_C}} \over {{I_E}}}$ & $\beta = {{{I_C}} \over {{I_B}}}$ & ${I_E} = {I_B} + {I_C}$<br><br>$\therefore$ ${{{I_E}} \over {{I_C}}} = {{{I_B}} \over {{I_C}}} + {{{I_C}} \over {{I_C}}}$<br><br>$$ \Rightarrow {1 \over \alpha } = {1 \over \beta } + 1 = {{1 + \beta } \over \beta }$$<br><br>$\Rightarrow \alpha = {\beta \over {1 + \beta }}$
About this question
Subject: Physics · Chapter: Electronic Devices · Topic: Semiconductors
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