How Do You Calculate Alpha and Beta DC in a Transistor?

[amaresh92]

1. Homework Statement [/b]
calculate alpha DC (emitter to collector dc current gain) and beta DC (base to collector dc current gain) for a transistor which has Ic=2.5ma, Ie=2.6ma .

Homework Equations

formula 1) alpha DC=Ic/Ie.
formula 2) beta DC =Ic/Ib.
formula 3) beta DC = alpha DC/(1-alpha DC)
formula 4) Ib=Ie-Ic

The Attempt at a Solution

using formula 1)

alpha dc=Ic/Ie

=2.5/2.6
=0.96

using formula 4)
Ib=Ie-Ic

=2.6-2.5
=0.1ma using formula 2)

beta DC =Ic/Ib

=2.5/0.1
=25

using formula 3)

beta DC = alpha DC/(1-alpha DC)

= 0.96/(1-0.96)

=24
my doubt is, from above calculation for beta DC using formula 2 and 3 we are getting two different values for beta DC. so which one is correct and under which condition or how i should use these two formula? In the sense when i should use formula 2 and formula 3.

advanced thanks

 

[Delta2]

The two formulas 2 and 3 can be proved easily that they are equal as long as we accept that the formulas 1 and 4 are valid and true.

BUT you get different results because you rounded up the result for alphaDC (alphaDC is not exactly 0.96 , if you use more decimal digits like 0.961538 you ll get betaDC closer to 25).

So be carefull when you round up results, or choose the formula that doesn't use rounded results. In this example formula 2 doesn't use rounded results because you know the exact values for Ib and Ic.