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A transistor is operated in common emitter configuration at constant collector voltage $V_c = 1.5$ V such that a change in the base current from 100 $\mu$A to 150 $\mu$A produces a change in the collector current from 5 mA to 10 mA. The current gain ($\beta$) is :-
A
67
B
75
C
100
D
50
Detailed Solution
The a.c. current gain in the common emitter configuration is $\beta = \dfrac{\Delta I_C}{\Delta I_B}$ at constant collector voltage.
$\Delta I_C = (10 - 5)$ mA $= 5 \times 10^{-3}$ A
$\Delta I_B = (150 - 100)\,\mu$A $= 50 \times 10^{-6}$ A
$\beta = \dfrac{(10 - 5) \times 10^{-3}}{(150 - 100) \times 10^{-6}}$
$\beta = \dfrac{5 \times 10^{-3}}{50 \times 10^{-6}} = 100$
$\Delta I_C = (10 - 5)$ mA $= 5 \times 10^{-3}$ A
$\Delta I_B = (150 - 100)\,\mu$A $= 50 \times 10^{-6}$ A
$\beta = \dfrac{(10 - 5) \times 10^{-3}}{(150 - 100) \times 10^{-6}}$
$\beta = \dfrac{5 \times 10^{-3}}{50 \times 10^{-6}} = 100$