Question

For a transistor, the value of \[\alpha \] is (\[\beta = 100.\]) ?
A. \[1.01\]
B. \[0.99\]
C. \[100\]
D. \[0.01\]

Answer 1

Hint:A transistor is a semiconductor device that amplifies or switches electrical power and electronic signals. It is made of semiconductor material and has at least three terminals for external circuit communication.

Complete step by step answer:
We should know the concepts related to the answer of the question. Alpha gain (\[\alpha \]) is the current gain in the common-base configuration, which is defined as the ratio of change in collector current to change in emitter current. A transistor's \[\alpha \] (alpha) is the element or value that is multiplied by an emitter current to get the collector current value.

The current gain in a typical Emitter configuration is known as beta gain (\[\beta \]). Beta gain is the current gain that is defined as the shift in collector current to base current.
\[\alpha = \dfrac{{{I_c}}}{{{I_E}}} \\
\Rightarrow \beta = \dfrac{{{I_c}}}{{{I_B}}} \\
{I_E}\,\text{is the emitter current}\,{I_B}\,\text{is the base current and}\,{I_c}\,\text{is the collector current} \\
\text{For a transistor we always have,} \\
{I_E}\, = {I_B} + {I_c} \\
\text{Dividing both side by}\,{I_c} \\
\dfrac{{{I_E}}}{{{I_c}}} = \dfrac{{{I_B}}}{{{I_c}}} + 1 \\
\text{Putting the value of}\,\alpha \,\text{and}\,\beta \\
\dfrac{1}{\alpha } = \dfrac{1}{\beta } + 1 \\
\Rightarrow \beta = \dfrac{\alpha }{{1 - \alpha }} \\
\Rightarrow \alpha = \dfrac{\beta }{{1 + \beta }} \\ \]
This is the relation between \[\alpha \] and \[\beta \]. We have \[\beta = 100.\]. Putting this value in the above equation,
\[\alpha = \dfrac{{100}}{{1 + 100}} \\
\alpha = \dfrac{{100}}{{101}} \\
\text{Value of}\,\alpha \,\text{is}\,\,\dfrac{{100}}{{101}} \\
\therefore \alpha = 0.99 \\ \]
So the correct option is B.

Additional Information:
Transistor is a n-p-n or p-n-p junction device. The central part is called the base and the other parts are called collector and emitter. The transistor can be designed in such a way that either collector or emitter or base is common to both the input and output.

Actually, This gives three common configurations called common emitter, common collector and common base transistor. For a transistor value of \[\alpha \] will be always less than\[1\], because then collector current is always less than emitter current. Again, the value of\[\beta \] is always greater than\[1\], because the value of collector current is always greater than base current.

Note:Consider which components are included in the question and which must be identified. If you can connect the dots, finding the answer would be a breeze. In the above question from the value of\[\beta \] we have found the value of \[\alpha \]. To find the other amounts, we followed the same procedure.