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

Hint: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.
\[\ \Rightarrow {I_c} = 19 \times 0.2 \\
   \Rightarrow {I_c} = 3.8mA \\
\ \]
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.