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Find the $\beta $ value of transistor if its $\alpha $ value is $0.9$.
(A) 9
(B) 0.9
(C) 0.09
(D) 90

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Last updated date: 20th Jun 2024
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Answer
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Hint The $\beta $ of the transistor is the gain or amplification factor of the transistor. It is the factor by which the current is amplified in the circuit. This factor for the transistor can be obtained by using the relation between $\alpha $ and $\beta $.
Formula used: - The relation between $\alpha $ and $\beta $ is –
$\alpha = \dfrac{\beta }{{\beta + 1}}$

Complete step by step solution
The semiconductor device which is used to amplify the electronic signals is called a transistor. A transistor is a type of a semiconductor device that can be used to both conduct and insulate electric current or voltage. A transistor basically acts as a switch and an amplifier. In simple words, we can say that a transistor is a miniature device that is used to control or regulate the flow of electronic signals.
The transistor is composed of three layers of semiconductor components. A voltage or current that is applied to any pair of terminals of the transistor controls the current through the pair of terminals. There are three terminals of the transistor:
Base – It is used to activate the transistor
Collector – This is the positive lead of the transistor
Emitter – This is the negative lead of the transistor
In the question, we have been given the two factors - $\alpha $ and $\beta $. So, let’s know something about it:
$\alpha $ factor of the transistor is the value that an emitter current is multiplied by to give the value of the collector current.
The $\beta $ of the transistor is the gain or amplification factor of the transistor. It is the factor by which the current is amplified in the circuit.
According to the question, it is given that –
$\alpha = 0.9$
The relation between $\alpha $ and $\beta $ is –
$
  \alpha = \dfrac{\beta }{{\beta + 1}} \\
   \Rightarrow \beta = \dfrac{\alpha }{{1 - \alpha }} \\
 $
Putting the value of $\alpha $ -
$
   \Rightarrow \beta = \dfrac{{0.9}}{{1 - 0.9}} \\
  \therefore \beta = 9 \\
 $
Hence, the value of $\beta $ is 0.9. Therefore, the correct option is (A).

Note If you have the value of emitter current of the transistor and you want to get the value of collector current then, the emitter current is multiplied by $\alpha $ to give the collector current.