Question

In a transistor if `I_c/I_e=alpha` and `I_c/I_b=beta`, if `alpha` varies between `(20)/(21)` and `(100)/(101)`, then the value of `beta` lied between?

Answer 1

`20 and 100`

Explanation:

Representative circuit in Common emitter amplifier configuration is given below

Given is the ratio of `I_c/I_b=beta`
And the ratio of `I_c/I_e= alpha`

From above expressions we have
`I_c=beta I_b=alphaI_e` .....(1)

In this configuration, the current flowing out of the transistor must be equal to the currents flowing into the transistor. As such we have

`I_e = I_c + I_b` .....(2)

To have a combined the expression for `α and β` we divide both sides of (2) by `I_b` and use (1) to get

`I_e/I_b = (I_c + I_b)/I_b`
`=>beta/alpha=beta+1`
`=>beta=alphabeta+alpha`

`=>beta=alpha/(1-alpha)`

For `alpha=20/21`

`beta=(20/21)/(1-20/21)=20`

Again for `alpha=100/101`
`beta=(100/101)/(1-100/101)=100`
.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-

Note: value of `alpha` will always be`<1`.
and typically, `beta` values lie between `20 and 200` for most general purpose transistors.