What are $\alpha$ and $\beta$ parameters for a transistor? Obtain a relation between them.

Hint: In order to solve this problem, we need to know that the Alpha of the transistor is the current gain in the common basic configuration defined as the ratio of the change in the collector current to the change in the emitter current while the beta is the current gain in the CE configuration. It is known as the change from collector current to base current.

Complete step-by-step answer:

Formula used - $\beta _{dc}$ ​=$\dfrac{{{I_C}}}{{{I_B}}}$, $\alpha _{dc}$= $\dfrac{{{I_c}}}{{{I_E}}}$.

Alpha=$\alpha_{d_C}$: This is known as the ratio of collector current to emitter current.
$\alpha _{dc}$= $\dfrac{{{I_c}}}{{{I_E}}}$ ………. (1)

Beta=$\beta _{d_c}$: This is the current gain specified as the ratio of collector current to base current.
$\beta _{dc}$ ​=$\dfrac{{{I_C}}}{{{I_B}}}$ ………. (2)

Relation between $\alpha _{dc}$and $\beta _{dc}$

For a transistor,
${I_B} = {I_c} + {I_E}$ ........ (3)
${I_c} \approx {I_E}$

Dividing both sides of equation (3)

By ${I_C}$ we get
$\dfrac{{{I_E}}}{{{I_C}}} = \dfrac{{{I_B}}}{{{I_C}}} + 1$
$ \Rightarrow \dfrac{1}{{\alpha _{dc}}} = \dfrac{1}{{\beta _{dc}}} + 1$
$\alpha _{dc} = \dfrac{{\beta _{dc}}}{{\beta _{dc} + 1}}$ .......... (4)
Or \[\beta _{dc} = \dfrac{{\alpha _{dc}}}{{1 - \alpha _{dc}}}\] ......... (5)

Equations (4) and (5) give the relation between $\alpha _{dc}$ and $\beta _{dc}$ ​of a transistor.

Transistors make excellent electronic switches. We can turn the currents on and off billions of times a second with the help of transistors. Digital computers use transistors as a basic mechanism for storing and moving data.

Note: During solving any problem knowing about it will clear your concept and help you solve some tricky problems. A transistor is a semiconductor device used to amplify or combine electrical and electronic signals. This is made of semiconductor material , typically having at least three terminals for connection to an external circuit. A transistor is a miniature electronic device that can perform two separate tasks. It can act either as an amplifier or as a switch: when it acts as an amplifier, it takes a tiny electrical current at one end (input current) and generates a much larger electrical current (output current) at the other.