Question

In the common base circuit of a transistor ,current amplification factor is 0.95. Calculate the emitter current if base current is 0.2 $mA$
A) 2 $mA$
B) 4$mA$
C) 6$mA$
D) 8$mA$

Answer 1

We have given the current amplification factor ($\alpha = 0.95$) and given base current ${I_b} = 0.2mA$ . First we will find the current gain $\beta$, then we will calculate the current at collector(${I_c}$) and in circuit of transistor we know that current at emitter is the sum of current at collector and base current ( ${I_e} = {I_b} + {I_c}$)

Formula used:- $\beta = \dfrac{{{I_c}}}{{{I_b}}}$, ${I_c}$is emitter current and ${I_b}$is the base current & $\beta$ is the current gain
$\beta = \dfrac{\alpha }{{1 - \alpha }}$, $\alpha$ is the current amplification factor & $\beta$ is the current gain
${I_e} = {I_b} + {I_c}$ , current at collector(${I_c}$) , base current (${I_b}$) , current at collector(${I_c}$)

current amplification factor $\alpha = 0.95$
base current ${I_b} = 0.2mA$
current gain $\beta = \dfrac{\alpha }{{1 - \alpha }}$
putting the value of $\alpha = 0.95$ in the formula $\beta = \dfrac{\alpha }{{1 - \alpha }}$ in order to find the current gain$\beta$.
$\Rightarrow \beta = \dfrac{{0.95}}{{1 - 0.95}} = \dfrac{{0.95}}{{0.5}} = 19$
And we also know that the current gain$\beta$is the ratio of current at collector to base current.
$\beta = \dfrac{{{I_c}}}{{{I_b}}}$
Now , we will find the value of current at collector ${I_c}$.
$\Rightarrow {I_c} = \beta .{I_b}$
Putting the values $\beta = 19$,${I_b} = 0.2mA$ and further simplifying.

\Rightarrow {I_c} = 3.8mA \\\ \ $$ Current at collector $${I_c} = 3.8mA$$ We have to find the emitter current $${I_e}$$, using the formula $${I_e} = {I_b} + {I_c}$$ $${I_e} = {I_b} + {I_c}$$ Putting the values $${I_b} = 0.2mA$$ & $${I_b} = 0.2mA$$ $$ \Rightarrow {I_e} = 3.8 + 0.2 = 4mA$$ Current at the common emitter is $$4mA$$. **Hence option (B) is the correct option.** **Note :-** In the common base circuit of a transistor current gain is always less than 1. In the common base circuit of a transistor input resistance is low. In the common base circuit of a transistor output resistance is very high. Common base configuration of the transistor is suitable for high frequency.