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JEE Mains Previous Years Questions with Solutions

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JEE Main 2016 (Offline)

MCQ (More than One Correct Answer)
For a common emitter configuration, if $$\alpha $$ and $$\beta $$ have their usual meanings, the incorrect relationship between $$\alpha $$ and $$\beta $$ is :
A
$$\alpha = {\beta \over {1 + \beta }}$$
B
$$\alpha = {{{\beta ^2}} \over {1 + {\beta ^2}}}$$
C
$${1 \over \alpha } = {1 \over \beta } + 1$$
D
$$\alpha = {\beta \over {1 - {\beta ^2}}}$$

Explanation

We know, collector current is given as $${I_C} = \beta {I_B}$$

Also, $${I_C} = \alpha {I_E}$$

​Using, $${I_E} = {I_B} + {I_C}$$

$${{{I_C}} \over \alpha } = {{{I_C}} \over \beta } + {I_C}$$

Solving above equations,

$${1 \over \alpha } = {1 \over \beta } + 1$$

$$\alpha = {\beta \over {1 + \beta }}$$

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