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Question

(C) We know that the current gain in common base configuration is $\alpha = \frac{I_C}{I_E}$ and in common emitter configuration is $\beta = \frac{I_C

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) We know that the current gain in common base configuration is $\alpha = \frac{I_C}{I_E}$ and in common emitter configuration is $\beta = \frac{I_C}{I_B}$.Since $I_E = I_B + I_C$,we can write $\alpha = \frac{I_C}{I_B + I_C}$.Dividing numerator and denominator by $I_B$,we get $\alpha = \frac{I_C/I_B}{1 + I_C/I_B} = \frac{\beta}{1 + \beta}$.From this,we can derive $\frac{1}{\alpha} = \frac{1 + \beta}{\beta} = \frac{1}{\beta} + 1$,which implies $\frac{1}{\alpha} - \frac{1}{\beta} = 1$ or $\frac{1}{\alpha} = \frac{1}{\beta} + 1$.Comparing the given options,option $C$ states $\alpha = \frac{\beta}{1 - \beta}$,which is incorrect because the correct relation is $\alpha = \frac{\beta}{1 + \beta}$.

For a common emitter configuration,if $\alpha$ and $\beta$ have their usual meanings,the incorrect relationship between $\alpha$ and $\beta$ is:

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