Question

In a transistor $\beta =100$ . The value of $\alpha$ is:

• A. 1
• B. 0.99
• C. 0.1
• D. 0.01

Answer 1

Answer: (B)

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.