Question #e4173

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Answer 1 · 2017-04-30T18:50:48

The current gain is $β = 49$ $beta = 49$

Given: $\frac{I_{0}}{I_{E}} = 0.98 [1]$ $I_0/I_E =0.98" [1]"$

We know that the output current is the current gain $β$ $beta$ multiplied by the base current:

$I_{0} = β I_{b} [2]$ $I_0 = betaI_b" [2]"$

We know that the emitter current is the output current plus the base current:

$I_{E} = I_{0} + I_{b}$ $I_E = I_0+ I_b$

$I_{E} = β I_{b} + I_{b} [3]$ $I_E = betaI_b+ I_b" [3]"$

Substitute equations [2] and [3] into equation [1]:

$\frac{β I_{b}}{β I_{b} + I_{b}} = 0.98$ $(betaI_b)/(betaI_b+I_b) = 0.98$

$\frac{β}{β + 1} = 0.98$ $beta/(beta+1) = 0.98$

$1 - \frac{1}{β + 1} = 0.98$ $1 -1/(beta+1) = 0.98$

beta+1 = -1/(0.98-1)

$β + 1 = 50$ $beta+1 = 50$

$β = 49$ $beta = 49$