Question

For a common base configuration of PNP transistor $\dfrac{{{\lambda _C}}}{{{\lambda _E}}} = 0.98$, then maximum current gain in common emitter configuration will be:
(A) $12$
(B) $49$
(C) $6$
(D) $5$

Answer 1

Hint:The input signal is applied between the emitter and base terminals while the corresponding output signal is taken across the collector and base terminals. Thus, the base terminal of a transistor is common for both input and output terminals and hence it is named as common base configuration. And by using the current gain in PNP transistor formula the solution can be determined.

Useful formula:
The current gain in the PNP transistor is given by,
$\beta = \dfrac{\alpha }{{1 - \alpha }}$
Where, $\beta $ is the current gain in the PNP transistor and $\alpha $ is the ratio of collector current to the emitter current.

Complete step by step solution:
Given that,
The ratio of the collector current to the emitter current is, $\dfrac{{{\lambda _C}}}{{{\lambda _E}}} = \alpha = 0.98$
Now,
The current gain in the PNP transistor is given by,
$\beta = \dfrac{\alpha }{{1 - \alpha }}\,......................\left( 1 \right)$
By substituting the ratio of collector current to the emitter current in the above equation (1), then the above equation (1) is written as,
$\beta = \dfrac{{0.98}}{{1 - 0.98}}$
By subtracting the terms in the denominator in the above equation, then the above equation is written as,
$\beta = \dfrac{{0.98}}{{0.02}}$
On dividing the above equation, then the above equation is written as,
$\beta = 49$
Thus, the above equation shows the current gain in the common emitter configuration.

Note: Current gain in the common emitter circuit is obtained from the base and the collector circuit currents. Because a very small change in base current produces a large change in collector current, the current gain $\beta $ is always greater than unity.