Define `alpha` and `beta` parameters of a transistor. What is the relation between them?

Explanation

The current gain in the common - emitter circuit is called beta `(beta)` . beta is the ratio of co,llector currect ot base current. To calculate beta, use the folowing formula :
`beta=I_(C)/I_(B)`
The currect gain in the common - base circuit is calculate3d in a method similar to that of the common emitter except that the imput current is `I_(E)` not `I_(B)` and the term alpha `(alpha)` is used in polce of beta for gain. Alpha is the ratio of collector current to current. Alpha is calculated by suing the formula:
`alpha=I_(C)/I_(E)`
Realation between `alpha` and `beta` :
As we know, from the working of the transistor.
`I_(E)=I_(B)+I_(C)`
On dividing both sides by `I_(C)`, we get
`I_(E)/I_(C)=I_(B)/I_(C)+1`
`"But "I_(C)/I_(B)=alpha" and "I_(C)/I_(B)=beta`
`1/alpha=1/beta+1`
`1/alpha=(1+beta)/beta` ltbtgt `"Tus, "alpha=beta/(beta+1)`