Thank you for reporting, we will resolve it shortly
Q.
In a transistor $ \beta =100 $ . The value of $ \alpha $ is:
Bihar CECEBihar CECE 2001Semiconductor Electronics: Materials Devices and Simple Circuits
Solution:
Current gain $ \alpha $ is defined for common-base transistor amplifier while $ \beta $ is defined for common-emitter transistor amplifier.
We have
$ \alpha =\frac{\Delta {{i}_{C}}}{\Delta {{i}_{E}}} $ ....(i)
and $ \beta =\frac{\Delta {{i}_{C}}}{\Delta {{i}_{B}}} $ ....(ii)
Also, $ {{i}_{E}}={{i}_{C}}+{{i}_{B}} $
$ \Rightarrow $ $ \Delta {{i}_{E}}=\Delta {{i}_{C}}+\Delta {{i}_{B}} $ ....(iii)
From Eq. (ii),
$ \beta =\frac{\Delta {{i}_{C}}}{\Delta {{i}_{B}}}=\frac{\Delta {{i}_{C}}}{\Delta {{i}_{E}}-\Delta {{i}_{C}}} $
or $ \beta =\frac{\Delta {{i}_{C}}/\Delta {{i}_{E}}}{1-\Delta {{i}_{C}}/\Delta {{i}_{E}}} $
or $ \beta =\frac{\alpha }{1-\alpha } $
or $ \alpha =\frac{\beta }{1+\beta } $ ....(iv)
Here, $ \beta =100 $
So, From Eq. (iv)
$ \alpha =\frac{100}{1+100}=0.99 $
Note: For a transistor amplifier, $ \alpha $ is about 0.95 to 0.99 and $ \beta $ is about 20 to 100.