First slide

Transistors

Question

For a common-emitter configuration, if $α$ and $β$ have their usual meanings, the correct relationship between $α$ and $β$ is

Moderate

A

$\frac{1}{α} = \frac{1}{β} + 2$
B

$α = \frac{β}{1 - β}$
C

$α = \frac{β}{1 + β}$
D

$α = \frac{β^{2}}{1 + β^{2}}$

Solution

As we know,
In case of a common emitter configuration, DC current gain, $α = \frac{I_{C}}{I_{E}}$ .
where, I_C is collector current and I_E is emitter current.
AC current gain, $β = \frac{I_{C}}{I_{B}}$ ………..(i)
where, l_B is base current.
Also, $I_{E} = I_{B} + I_{C}$ …….(ii)
Dividing Eq. (i) by I_C, we get
$\begin{array}{l} \Rightarrow \frac{I_{E}}{I_{C}} = \frac{I_{B}}{I_{C}} + 1 [from Eq . (i)] \\ \Rightarrow \frac{1}{α} = \frac{1}{β} + 1 \Rightarrow α = \frac{β}{1 + β} \end{array}$

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