Question

The current gain in the common emitter amplifier is $59$. If the emitter current is $6.0mA$, find, (i) base current (ii) collector current.

Answer 1

Step 1. Given data:

For a common emitter amplifier,

Current gain in CE amplifier $\left(\beta \right)=59$

Emitter current $\left(I_e\right)$=$6.0mA$

Let $I_c$= Collector current

$I_b$= Base current

Step 2. Formula used:

Current gain in CE amplifier $\left(\beta \right)$=$\left(I_c-I_b\right)/\left(I_b\right)=\frac{I_c}{I_b}-1$

or $I_b=\frac{I_c}{1+\beta }$

Also current gain in CB amplifier $\alpha =\frac{\beta }{1+\beta }$ and $I_c=\alpha I_e$

Step 3. Calculations:

Because current gain $\Rightarrow \alpha =\frac{\beta }{1+\beta }=\frac{59}{60}$

$$\begin{gathered} \alpha =\frac{I_c}{I_e}\Rightarrow I_c=\alpha I_e \\ {I}_c=\frac{59}{60}\times 6=5.9mA \end{gathered}$$

Now base current $I_b=\frac{I_c}{1+\beta }=\frac{5.9}{1+59}=0.1mA$

Hence, the base current is $0.1mA$ and the collector current is $5.9mA$.