Question

In a common-base mode of a transistor, the collector current is \[5.488{\text{ }}mA\] for an emitter current of \[5.60{\text{ }}mA\]. The value of the base current amplification factor\[\left( \beta \right)\]will be
A. \[49\]
B. \[50\]
C. \[51\]
D. \[48\]

Answer 1

Hint: In common base, the configuration emitter is the input terminal and the collector is the output terminal. The base terminal will be connected to both input and output as a common terminal. Then the input terminals will be emitter and common base terminals and the output terminals will be the collector and common base terminals.

Complete step by step solution:
A transistor consists of three-part- a collector, emitter, and base. It is a semiconductor device made by fusing two junction diodes.
The amplification of the current is determined by the current amplification factor and it is also called the current gain. The ratio of the change in the collector current to the change on the base current is called the base current amplification factor.
\[\beta = \dfrac{{{{\text{I}}_{\text{C}}}}}{{{{\text{I}}_{\text{B}}}}}\]
Here\[\beta \]is the base current amplification factor.
 \[{{\text{I}}_{\text{C}}}\] is the collector current
\[{{\text{I}}_{\text{B}}}\] isthe base current.
We know that the emitter current\[{I_E}\] is equal to the base current \[{I_B}\] and collector current \[{I_C}\].
\[{I_E} = {I_B} + {I_C}\]
In the question given that,
\[{I_E}\], the emitter current is equal to\[5.60{\text{ }}mA\], and\[{I_C}\], the collector current is equal to\[5.488{\text{ }}mA\].
Now rearranging the above equation to get the base current we get,
\[{I_B} = {I_E} - {I_C}\]
Substituting all the known values that are given to us in the question in the above equation,
\[{I_B} = 5.60 - 5.488\]
\[{I_B} = 0.112mA\]
Thus substituting this base current value in the base current amplification factor formula, we get,
\[\beta = \dfrac{{5.488{\text{ }}mA}}{{0.112mA}}\]
\[\beta = 49\]
Therefore it is the value for the base current amplification factor.

Note:
The ratio of the collector current (\[{I_C}\]) to the emitter current (\[{I_E}\]) when the collector voltage (\[{{\text{V}}_{{\text{CB}}}}\]) which is applied between collector and base is kept constant is known as the current amplification factor. It is denoted by\[\alpha \].
At constant collector voltage (\[{{\text{V}}_{{\text{CB}}}}\]).
Current amplification factor\[\alpha = \dfrac{{{I_C}}}{{{I_E}}}\].
Since it is a ratio between two values it does not have any unit.