# Question #e4173

Apr 30, 2017

The current gain is $\beta = 49$

#### Explanation:

Given: ${I}_{0} / {I}_{E} = 0.98 \text{ [1]}$

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

${I}_{0} = \beta {I}_{b} \text{ [2]}$

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

${I}_{E} = {I}_{0} + {I}_{b}$

${I}_{E} = \beta {I}_{b} + {I}_{b} \text{ [3]}$

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

$\frac{\beta {I}_{b}}{\beta {I}_{b} + {I}_{b}} = 0.98$

$\frac{\beta}{\beta + 1} = 0.98$

$1 - \frac{1}{\beta + 1} = 0.98$

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

$\beta + 1 = 50$

$\beta = 49$